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Ralph Byers and
Stephen Nash On the singular ``vectors'' of the
Lyapunov operator . . . . . . . . . . . 59--66
Richard A. Brualdi Dedication . . . . . . . . . . . . . . . iv--v
Daniel Hershkowitz and
Hans Schneider Equality classes of matrices . . . . . . 1--18
Clark Jeffries and
Charles R. Johnson Some sign patterns that preclude matrix
stability . . . . . . . . . . . . . . . 19--25
Joseph W. H. Liu A tree model for sparse symmetric
indefinite matrix factorization . . . . 26--39
Peter Arbenz and
Gene H. Golub On the Spectral Decomposition of
Hermitian Matrices Modified by Low Rank
Perturbations with Applications . . . . 40--58
Gregory S. Ammar and
William B. Gragg Superfast solution of real positive
definite Toeplitz systems . . . . . . . 61--76
T. Beelen and
P. Van Dooren A pencil approach for embedding a
polynomial matrix into a unimodular
matrix . . . . . . . . . . . . . . . . . 77--89
Dipa Choudhury and
Roger A. Horn An analogue of the Schur triangular
factorization for complex orthogonal
similarity and consimilarity . . . . . . 90--95
Roberto Cristi Parallel processing in the adaptive
control of linear systems . . . . . . . 96--105
Victor E. DeBrunner and
A. A. (Louis) Beex Sensitivity analysis of digital filter
structures . . . . . . . . . . . . . . . 106--125
James Demmel and
Bo Kågström Accurate solutions of ill-posed problems
in control theory . . . . . . . . . . . 126--145
C. A. Butler and
T. D. Morley A note on the shorted operator . . . . . 147--155
Dennis S. Bernstein Inequalities for the trace of matrix
exponentials . . . . . . . . . . . . . . 156--158
Charles R. Johnson and
Leiba Rodman Completion of Toeplitz partial
contractions . . . . . . . . . . . . . . 159--167
G. P. Barker and
S.-J. Yang Semi-iterative and iterative methods for
singular $ {M}$-matrices . . . . . . . . 168--180
William F. Trench Toeplitz systems associated with the
product of a formal Laurent series and a
Laurent polynomial . . . . . . . . . . . 181--193
Robert Grone and
Stephen Pierce Permanental inequalities for correlation
matrices . . . . . . . . . . . . . . . . 194--201
Heinrich Bolz and
Wilhelm Niethammer On the evaluation of matrix functions
given by power series . . . . . . . . . 202--209
Daniel R. Fuhrmann An algorithm for subspace computation,
with applications in signal processing 213--220
Volker Mehrmann A symplectic orthogonal method for
single input or single output discrete
time optimal quadratic control problems 221--247
P. Misra and
R. V. Patel A determinant identity and its
application in evaluating frequency
response matrices . . . . . . . . . . . 248--255
Michael L. Overton On minimizing the maximum eigenvalue of
a symmetric matrix . . . . . . . . . . . 256--268
Charles M. Rader and
Allan O. Steinhardt Hyperbolic Householder transforms . . . 269--290
William F. Trench Numerical solution of the eigenvalue
problem for symmetric rationally
generated Toeplitz matrices . . . . . . 291--303
Paul D. Gader Necessary and sufficient conditions for
the existence of local matrix
decompositions . . . . . . . . . . . . . 305--313
Harald K. Wimmer Extremal problems for Hölder norms of
matrices and realizations of linear
systems . . . . . . . . . . . . . . . . 314--322
San Zheng Qiao Recursive least squares algorithm for
linear prediction problems . . . . . . . 323--328
G. Avdelas and
J. de Pillis and
A. Hadjidimos and
M. Neumann A guide to the acceleration of iterative
methods whose iteration matrix is
nonnegative and convergent . . . . . . . 329--342
Miroslav Fiedler and
Thomas L. Markham On the range of the Hadamard product of
a positive definite matrix and its
inverse . . . . . . . . . . . . . . . . 343--347
Jean H. Bevis and
Frank J. Hall and
Robert E. Hartwig The matrix equation $ A \overline X - X
B = C $ and its special cases . . . . . 348--359
Sabine Van Huffel and
Joos Vandewalle Analysis and solution of the nongeneric
total least squares problem . . . . . . 360--372
Ron Perline Self-dual polynomials, Hermite matrices,
and Heisenberg functionals . . . . . . . 373--377
A. Shapiro and
J. D. Botha Dual algorithms for orthogonal
Procrustes rotations . . . . . . . . . . 378--383
Thomas M. Cover and
Joy A. Thomas Determinant inequalities via information
theory . . . . . . . . . . . . . . . . . 384--392
Pablo M. Salzberg Tomography in projective spaces: a
heuristic for limited angle
reconstructive models . . . . . . . . . 393--398
David L. Powers Eigenvectors of distance-regular graphs 399--407
Jeffrey L. Stuart Inflation matrices and $ {\rm ZME}
$-matrices that commute with a
permutation matrix . . . . . . . . . . . 408--418
S. Lennart Johnsson and
Ching-Tien Ho Algorithms for matrix transposition on
Boolean $ {N}$-cube configured ensemble
architectures . . . . . . . . . . . . . 419--454
Daniel Hershkowitz and
Uriel G. Rothblum and
Hans Schneider Classifications of nonnegative matrices
using diagonal equivalence . . . . . . . 455--460
Stephen Pierce and
Leiba Rodman Linear preservers of the class of
Hermitian matrices with balanced inertia 461--472
Michael L. Overton and
Robert S. Womersley On minimizing the spectral radius of a
nonsymmetric matrix function: optimality
conditions and duality theory . . . . . 473--498
Paolo Bolzern and
Patrizio Colaneri The periodic Lyapunov equation . . . . . 499--512
Ronald K. Pearson Block-sequential algorithms for
set-theoretic estimation . . . . . . . . 513--527
Moody T. Chu and
T.-Y. Li and
Tim Sauer Homotopy method for general $ \lambda
$-matrix problems . . . . . . . . . . . 528--536
Charles M. Grinstead Cycle lengths in $ {A}^k b $ . . . . . . 537--542
Alan Edelman Eigenvalues and condition numbers of
random matrices . . . . . . . . . . . . 543--560
Maria Célia Santos A note on the Newton iteration for the
algebraic eigenvalue problem . . . . . . 561--569
Harald K. Wimmer Linear matrix equations, controllability
and observability, and the rank of
solutions . . . . . . . . . . . . . . . 570--578
Robert B. Marr and
George H. Vineyard Five-diagonal Toeplitz determinants and
their relation to Chebyshev polynomials 579--586
C. T. Pan and
Kermit Sigmon A sharp bound for products of hyperbolic
plane rotations . . . . . . . . . . . . 587--593
Tongwen Chen and
Bruce A. Francis Spectral and inner-outer factorizations
of rational matrices . . . . . . . . . . 1--17
David C. Hyland and
Emmanuel G. Collins, Jr. Block Kronecker products and block norm
matrices in large-scale systems analysis 18--29
John E. Mitchell and
Michael J. Todd A variant of Karmarkar's linear
programming algorithm for problems with
some unrestricted variables . . . . . . 30--38
Hsin-Chu Chen and
Ahmed H. Sameh A matrix decomposition method for
orthotropic elasticity problems . . . . 39--64
Eric C. Howe and
Charles R. Johnson Linear aggregation of input-output
models . . . . . . . . . . . . . . . . . 65--79
Christopher Beattie and
David W. Fox Localization criteria and containment
for Rayleigh quotient iteration . . . . 80--93
Charles R. Johnson and
D. D. Olesky and
P. van den Driessche Inherited matrix entries: $ {LU} $
factorizations . . . . . . . . . . . . . 94--104
Giles Auchmuty Variational principles for eigenvalues
of nonsymmetric matrices . . . . . . . . 105--117
Bernard F. Lamond and
Martin L. Puterman Generalized inverses in discrete time
Markov decision processes . . . . . . . 118--134
William F. Trench Numerical solution of the eigenvalue
problem for Hermitian Toeplitz matrices 135--146
Ion Zaballa Invariant factor assignment on
higher-order systems using
state-feedback . . . . . . . . . . . . . 147--154
Nicholas J. Higham and
Desmond J. Higham Large growth factors in Gaussian
elimination with pivoting . . . . . . . 155--164
Mario Arioli and
James W. Demmel and
Iain S. Duff Solving sparse linear systems with
sparse backward error . . . . . . . . . 165--190
Charles Kenney and
Alan J. Laub Condition estimates for matrix functions 191--209
J. Philip Kavanagh and
Michael Neumann Consistency and convergence of the
parallel multisplitting method for
singular $ {M}$-matrices . . . . . . . . 210--218
M. Hegland and
J. T. Marti Algorithms for the reconstruction of
special Jacobi matrices from their
eigenvalues . . . . . . . . . . . . . . 219--228
Walter D. Morris, Jr. and
Jim Lawrence Geometric properties of hidden Minkowski
matrices . . . . . . . . . . . . . . . . 229--232
Yoo Pyo Hong A canonical form for Hermitian matrices
under complex orthogonal congruence . . 233--243
D. S. Watkins and
L. Elsner Self-equivalent flows associated with
the singular value decomposition . . . . 244--258
Layne T. Watson and
J. Patrick Bixler and
Aubrey B. Poore Continuous homotopies for the linear
complementarity problem . . . . . . . . 259--277
L. Jódar and
E. Navarro Co-square roots of matrices and their
application to boundary value
differential matrix problems . . . . . . 279--286
Moshe Haviv More on Rayleigh--Ritz refinement
technique for nearly uncoupled
stochastic matrices . . . . . . . . . . 287--293
Sabine Van Huffel and
Joos Vandewalle Analysis and properties of the
generalized total least squares problem
$ A X \approx B $ when some or all
columns in $ {A} $ are subject to error 294--315
I. Gohberg and
M. A. Kaashoek and
A. C. M. Ran Partial pole and zero displacement by
cascade connection . . . . . . . . . . . 316--325
Gautam Shroff and
Robert Schreiber On the convergence of the cyclic Jacobi
method for parallel block orderings . . 326--346
J. C. Allwright On maximizing the minimum eigenvalue of
a linear combination of symmetric
matrices . . . . . . . . . . . . . . . . 347--382
Sankar Basu Padé approximants to matrix Stieltjes
series: convergence and related
properties . . . . . . . . . . . . . . . 383--406
J. W. Helton and
S. Pierce and
L. Rodman The ranks of extremal positive
semidefinite matrices with given
sparsity pattern . . . . . . . . . . . . 407--423
J. L. Nazareth Updating the triangular factorization of
a matrix . . . . . . . . . . . . . . . . 424--428
R. B. Bapat Majorization and singular values. II . . 429--434
Chi-Kwong Li and
Nam-Kiu Tsing $ {G}$-invariant Hermitian forms and $
{G}$-invariant elliptical norms . . . . 435--445
Christopher L. Cox and
William F. Moss Backward error analysis for a pole
assignment algorithm . . . . . . . . . . 446--456
Chong Gu and
Douglas M. Bates and
Ze Hua Chen and
Grace Wahba The computation of generalized
cross-validation functions through
Householder tridiagonalization with
applications to the fitting of
interaction spline models . . . . . . . 457--480
R. E. White Multisplitting with different weighting
schemes . . . . . . . . . . . . . . . . 481--493
James R. Bunch and
James W. Demmel and
Charles F. Van Loan The strong stability of algorithms for
solving symmetric linear systems . . . . 494--499
John S. Maybee and
D. D. Olesky and
P. van den Driessche and
G. Wiener Matrices, digraphs, and determinants . . 500--519
Jeffrey L. Stuart An eigenvector test for inflation
matrices and $ {\rm {ZME}}$-matrices . . 520--532
Ji Guang Sun A note on local behavior of multiple
eigenvalues . . . . . . . . . . . . . . 533--541
Raymond H. Chan Circulant preconditioners for Hermitian
Toeplitz systems . . . . . . . . . . . . 542--550
Stephen Barnett Leverrier's algorithm: a new proof and
extensions . . . . . . . . . . . . . . . 551--556
Richard Bartels and
Linda Kaufman Cholesky factor updating techniques for
rank $2$ matrix modifications . . . . . 557--592
David C. Hyland and
Emmanuel G. Collins, Jr. Erratum: ``Block Kronecker products and
block norm matrices in large-scale
systems analysis'' [SIAM J. Matrix Anal.
Appl. \bf 10 (1989), no. 1, 18--29 and
MR 90a:93010] . . . . . . . . . . . . . 593--593
R. J. Plemmons and
R. E. White Substructuring Methods for Computing the
Nullspace of Equilibrium Matrices . . . 1--22
Nicholas J. Higham Stability Analysis of Algorithms for
Solving Confluent Vandermonde-like
Systems . . . . . . . . . . . . . . . . 23--41
K. S. Arun and
S. Y. Kung Balanced Approximation of Stochastic
Systems . . . . . . . . . . . . . . . . 42--68
R. E. White Multisplitting of a Symmetric Positive
Definite Matrix . . . . . . . . . . . . 69--82
Piotr Berman and
Georg Schnitger On the Performance of the Minimum Degree
Ordering for Gaussian Elimination . . . 83--88
Jürgen Garloff Block Methods for the Solution of Linear
Interval Equations . . . . . . . . . . . 89--106
Raphael Loewy Linear Maps That Preserve an Inertia
Class . . . . . . . . . . . . . . . . . 107--112
Tie Jun Li and
S. F. McCormick The Realization Problem for a Class of
Nonlinear Systems . . . . . . . . . . . 113--127
Richard D. Hill and
Ronald G. Bates and
Steven R. Waters On Centro-Hermitian Matrices . . . . . . 128--133
Joseph W. H. Liu The Role of Elimination Trees in Sparse
Factorization . . . . . . . . . . . . . 134--172
Richard D. Hill and
Ronald G. Bates and
Steven R. Waters On Per-Hermitian Matrices . . . . . . . 173--179
L. H. Keel and
S. P. Bhattacharyya A Matrix Equation Approach to the Design
of Low-Order Regulators . . . . . . . . 180--199
Chi Fai Ho Some $0$--$1$ Solutions to Matrix
Equation $ {A}^m - {A}^n = {IJ}$ ---
Part I . . . . . . . . . . . . . . . . . 200--206
W. N. Anderson, Jr. and
T. D. Morley and
G. E. Trapp Sets of Positive Operators with Suprema 207--212
Irving Kaplansky Algebraic Polar Decomposition . . . . . 213--217
Robert Grone and
Russell Merris and
V. S. Sunder The Laplacian Spectrum of a Graph . . . 218--238
Dennis S. Bernstein and
Wassim M. Haddad Robust Stability and Performance
Analysis for State-Space Systems via
Quadratic Lyapunov Bounds . . . . . . . 239--271
Rajendra Bhatia and
Fuad Kittaneh On the Singular Values of a Product of
Operators . . . . . . . . . . . . . . . 272--277
Inmaculada de Hoyos Points of Continuity of the Kronecker
Canonical Form . . . . . . . . . . . . . 278--300
D. S. Watkins and
L. Elsner On Rutishauser's Approach to
Self-Similar Flows . . . . . . . . . . . 301--311
Christian H. Bischof Incremental Condition Estimation . . . . 312--322
Roger G. Grimes and
Daniel J. Pierce and
Horst D. Simon A New Algorithm for Finding a
Pseudoperipheral Node in a Graph . . . . 323--335
Lloyd N. Trefethen and
Robert S. Schreiber Average-Case Stability of Gaussian
Elimination . . . . . . . . . . . . . . 335--360
Devendra Chhetry and
Jan de Leeuw and
Allan R. Sampson Monotone Correlation and Monotone
Disjunct Pieces . . . . . . . . . . . . 361--368
Marvin D. Troutt An Eigenvalue Formula for the Radius of
Stability of a Stable Game Matrix . . . 369--372
M. Seetharama Gowda Affine Pseudomonotone Mappings and the
Linear Complementarity Problem . . . . . 373--380
J. G. Lewis and
J. R. Gilbert and
R. J. Plemmons and
H. D. Simon Preface to the Special Section on Sparse
Matrices . . . . . . . . . . . . . . . . 381--381
Timothy A. Davis and
Pen-Chung Yew A nondeterministic parallel algorithm
for general unsymmetric sparse $ {LU} $
factorization . . . . . . . . . . . . . 383--402
C.-C. Jay Kuo and
Tony F. Chan and
Charles Tong Multilevel filtering elliptic
preconditioners . . . . . . . . . . . . 403--429
Alex Pothen and
Horst D. Simon and
Kang-Pu Liou Partitioning sparse matrices with
eigenvectors of graphs . . . . . . . . . 430--452
Eleanor Chu and
Alan George Sparse orthogonal decomposition on a
hypercube multiprocessor . . . . . . . . 453--465
Dianne P. O'Leary Robust regression computation using
iteratively reweighted least squares . . 466--480
Gene Golub and
Bo Kågström and
Axel Ruhe and
Paul Van Dooren Dedication to Vera N. Kublanovskaya on
her 70th Birthday . . . . . . . . . . . vii--ix
Roger A. Horn and
Roy Mathias An Analog of the Cauchy--Schwarz
Inequality for Hadamard Products and
Unitarily Invariant Norms . . . . . . . 481--498
G. Cybenko and
M. Berry Hyperbolic Householder Algorithms for
Factoring Structured Matrices . . . . . 499--520
Nicholas J. Higham Bounding the Error in Gaussian
Elimination for Tridiagonal Systems . . 521--530
Paul Binding Simultaneous Diagonalisation of Several
Hermitian Matrices . . . . . . . . . . . 531--536
Dario Bini and
Fabio Di Benedetto Solving the Generalized Eigenvalue
Problem for Rational Toeplitz Matrices 537--552
Yitsak M. Ram and
Joab J. Blech and
Simon G. Braun Eigenproblem Error Bounds with
Application to Symmetric Dynamic System
Modification . . . . . . . . . . . . . . 553--564
Daniel Hershkowitz and
Hans Schneider On the Inertia of Intervals of Matrices 565--574
Jesse L. Barlow and
Udaya B. Vemulapati An Improved Method for One-Way
Dissection with Singular Diagonal Blocks 575--588
W. Glunt and
T. L. Hayden and
S. Hong and
J. Wells An Alternating Projection Algorithm for
Computing the Nearest Euclidean Distance
Matrix . . . . . . . . . . . . . . . . . 589--600
William F. Trench Spectral Evolution of a One-Parameter
Extension of a Real Symmetric Toeplitz
Matrix . . . . . . . . . . . . . . . . . 601--611
Daniel Hershkowitz Positive Semidefinite Pattern
Decompositions . . . . . . . . . . . . . 612--619
A. Hadjidimos and
D. Noutsos The Young--Eidson Algorithm:
Applications and Extensions . . . . . . 620--631
Daniel Boley Estimating the Sensitivity of the
Algebraic Structure of Pencils with
Simple Eigenvalue Estimates . . . . . . 632--643
Christian H. Bischof and
John G. Lewis and
Daniel J. Pierce Incremental Condition Estimation for
Sparse Matrices . . . . . . . . . . . . 644--659
Charles R. Johnson and
Peter Nylen Largest Singular Value
Submultiplicativity . . . . . . . . . . 1--6
Jeffrey L. Stuart Determinants of Hessenberg $
{L}$-Matrices . . . . . . . . . . . . . 7--15
Ion Zaballa Pole Assignment and Additive
Perturbations of Fixed Rank . . . . . . 16--23
Alfred Bruckstein and
Thomas Kailath and
Israel Koltracht and
Peter Lancaster On the Reconstruction of Layered Media
from Reflection Data . . . . . . . . . . 24--40
Adam W. Boja\'nczyk and
Adam Lutoborski Computation of the Euler Angles of a
Symmetric $ 3 \times 3 $ Matrix . . . . 41--48
Marvin Marcus and
Markus Sandy Hadamard Square Roots . . . . . . . . . 49--69
Stephen Pierce and
Leiba Rodman On Simultaneous Congruence and Norms of
Hermitian Matrices . . . . . . . . . . . 70--83
Ivan Slapni\vcar and
Vjeran Hari On the Quadratic Convergence of the
Falk--Langemeyer Method . . . . . . . . 84--114
Moody T. Chu Least Squares Approximation by Real
Normal Matrices with Specified Spectrum 115--127
J. Chun and
T. Kailath Divide-and-Conquer Solutions of
Least-Squares Problems for Matrices with
Displacement Structure . . . . . . . . . 128--145
Nam-Kiu Tsing and
Frank Uhlig Inertia, Numerical Range, and Zeros of
Quadratic Forms for Matrix Pencils . . . 146--159
Ronald J. Stern and
Henry Wolkowicz Exponential Nonnegativity on the Ice
Cream Cone . . . . . . . . . . . . . . . 160--165
Mordechai Lewin Nonnegative Idempotent Matrices and
Their Graphs . . . . . . . . . . . . . . 166--171
Hong Yuan Zha The Restricted Singular Value
Decomposition of Matrix Triplets . . . . 172--194
Roger A. Horn and
Chi-Kwong Li and
Nam-Kiu Tsing Linear Operators Preserving Certain
Equivalence Relations on Matrices . . . 195--204
G. W. Stewart Two Simple Residual Bounds for the
Eigenvalues of a Hermitian Matrix . . . 205--208
Abraham Berman and
Dafna Shasha Inertia-Preserving Matrices . . . . . . 209--219
P. Delsarte and
Y. Genin Tridiagonal Approach to the Algebraic
Environment of Toeplitz Matrices. Part
I: Basic Results . . . . . . . . . . . . 220--238
R. B. Holmes On Random Correlation Matrices . . . . . 239--272
Charles Kenney and
Alan J. Laub Rational Iterative Methods for the
Matrix Sign Function . . . . . . . . . . 273--291
Sabine Van Huffel and
Hong Yuan Zha The Restricted Total Least Squares
Problem: Formulation, Algorithm, and
Properties . . . . . . . . . . . . . . . 292--309
I. Koltracht and
M. Neumann On the Inverse $ {M}$-Matrix Problem for
Real Symmetric Positive-Definite
Toeplitz Matrices . . . . . . . . . . . 310--320
Ronald Perline Toeplitz Matrices and Commuting
Tridiagonal Matrices . . . . . . . . . . 321--326
Sylvan Elhay and
Gene H. Golub and
Jaroslav Kautský Updating and Downdating of Orthogonal
Polynomials with Data Fitting
Applications . . . . . . . . . . . . . . 327--353
Nick Gould On Growth in Gaussian Elimination with
Complete Pivoting . . . . . . . . . . . 354--361
George A. Geist Reduction of a General Matrix to
Tridiagonal Form . . . . . . . . . . . . 362--373
D. S. Watkins and
L. Elsner Chasing Algorithms for the Eigenvalue
Problem . . . . . . . . . . . . . . . . 374--384
G. S. Miminis and
C. C. Paige Implicit Shifting in the $ Q R $ and
Related Algorithms . . . . . . . . . . . 385--400
Bart L. R. De Moor and
Gene H. Golub The Restricted Singular Value
Decomposition: Properties and
Applications . . . . . . . . . . . . . . 401--425
Gregory S. Ammar and
William B. Gragg $ {O}(n^2) $ Reduction Algorithms for
the Construction of a Band Matrix from
Spectral Data . . . . . . . . . . . . . 426--431
P. Delsarte and
Y. Genin Tridiagonal Approach to the Algebraic
Environment of Toeplitz Matrices. Part
II: Zero and Eigenvalue Problems . . . . 432--448
Jeffrey C. Lagarias Monotonicity properties of the Toda
flow, the $ Q R $-flow, and subspace
iteration . . . . . . . . . . . . . . . 449--462
P. A. Deift and
S. Rivera and
C. Tomei and
D. S. Watkins A Monotonicity Property for Toda-Type
Flows . . . . . . . . . . . . . . . . . 463--468
W. Govaerts Stable Solvers and Block Elimination for
Bordered Systems . . . . . . . . . . . . 469--483
Stephen L. Campbell and
William J. Terrell Observability of Linear Time-Varying
Descriptor Systems . . . . . . . . . . . 484--496
Y. Bistritz and
H. Lev-Ari and
T. Kailath Immitance-Type Three-Term Schur and
Levinson Recursions for Quasi-Toeplitz
Complex Hermitian Matrices . . . . . . . 497--520
M. E. Sezer and
D. D. \vSiljak Nested Epsilon Decompositions of Linear
Systems: Weakly Coupled and Overlapping
Blocks . . . . . . . . . . . . . . . . . 521--533
Gregory Ammar and
Paul Gader A Variant of the Gohberg--Semencul
Formula Involving Circulant Matrices . . 534--540
M. J. C. Gover Properties of the Inverse of the
Gaussian Matrix . . . . . . . . . . . . 541--548
D. J. Evans and
C. Li New Stopping Criteria for Some Iterative
Methods for a Class of Unsymmetric
Linear Systems . . . . . . . . . . . . . 549--551
Lothar Reichel Fast $ Q R $ Decomposition of
Vandermonde-like Matrices and Polynomial
Least Squares Approximation . . . . . . 552--564
Maite Gassó and
Vicente Hernández Factorization Problems for Nonmonic
Matrix Polynomials . . . . . . . . . . . 565--576
Czes\law St\kepniak Inversion of Covariance Matrices:
Explicit Formulae . . . . . . . . . . . 577--580
A. Bülent Özgüler The equation $ A X B + C Y D = E $ over
a principal ideal domain . . . . . . . . 581--591
Ezio Marchi and
Jorge A. Oviedo and
Joel E. Cohen Perturbation Theory of a Nonlinear Game
of von Neumann . . . . . . . . . . . . . 592--596
Ya Yan Lu and
Shing-Tung Yau Eigenvalues of the Laplacian through
Boundary Integral Equations . . . . . . 597--609
Jong-Shi Pang Iterative descent algorithms for a row
sufficient linear complementarity
problem . . . . . . . . . . . . . . . . 611--624
O. Axelsson and
P. S. Vassilevski A Black Box Generalized Conjugate
Gradient Solver with Inner Iterations
and Variable-Step Preconditioning . . . 625--644
Siegfried M. Rump A class of arbitrarily ill-conditioned
floating-point matrices . . . . . . . . 645--653
Shou Gen Wang and
Shu Qin Zhao An Algorithm for $ A x = \lambda B x $
with Symmetric and Positive-Definite $A$
and $B$ . . . . . . . . . . . . . . . . 654--660
Jerome Dancis Diagonalizing the Adaptive SOR Iteration
Method . . . . . . . . . . . . . . . . . 661--678
Antonie Stam and
Steven C. Hillmer Order Reductions of the Marginals and
Identification of Multiple ARMA Models 679--689
Giles Auchmuty Globally and Rapidly Convergent
Algorithms for Symmetric Eigenproblems 690--706
Ezio Marchi The Effective Computation of Equilibrium
Point for $ {N}$-Person Games Cyclic to
the Next Person . . . . . . . . . . . . 707--712
B. Yang and
J. F. Böhme Reducing the Computations of the
Singular Value Decomposition Array Given
by Brent and Luk . . . . . . . . . . . . 713--725
Harry H. Tigelaar On Monotone Linear Operators and the
Spectral Radius of Their Representing
Matrices . . . . . . . . . . . . . . . . 726--729
A. L. Forsgren and
P. E. Gill and
W. Murray On the Identification of Local
Minimizers in Inertia-Controlling
Methods for Quadratic Programming . . . 730--746
Kazuo Murota On the Smith Normal Form of Structured
Polynomial Matrices . . . . . . . . . . 747--765
Steven F. Ashby Minimax polynomial preconditioning for
Hermitian linear systems . . . . . . . . 766--789
Chi-Kwong Li Some Inequalities on the Decomposable
Numerical Radii of Matrices . . . . . . 790--801
Cleve Moler Dedication to Gene H. Golub on the
occasion of his 15th birthday . . . . . vii--viii
Jewel B. Barlow and
Moghen M. Monahemi and
Dianne P. O'Leary Constrained matrix Sylvester equations 1--9
James Demmel The Componentwise Distance to the
Nearest Singular Matrix . . . . . . . . 10--19
Sabine Van Huffel On the Significance of Nongeneric Total
Least Squares Problems . . . . . . . . . 20--35
Richard A. Brualdi and
Keith L. Chavey Sign-Nonsingular Matrix Pairs . . . . . 36--40
Michael L. Overton and
Robert S. Womersley On the Sum of the Largest Eigenvalues of
a Symmetric Matrix . . . . . . . . . . . 41--45
Angelika Bunse-Gerstner and
Volker Mehrmann and
Nancy K. Nichols Regularization of Descriptor Systems by
Derivative and Proportional State
Feedback . . . . . . . . . . . . . . . . 46--67
Linda Kaufman and
Garrett Sylvester Separable Nonlinear Least Squares with
Multiple Right-Hand Sides . . . . . . . 68--89
Bo Kågström and
Peter Poromaa Distributed and shared memory block
algorithms for the triangular Sylvester
equation with $ {\rm sep}^{-1} $
estimators . . . . . . . . . . . . . . . 90--101
Sofoklis Galanis and
Apostolos Hadjidimos Best Cyclic Repartitioning for Optimal
Successive Overrelaxation Convergence 102--120
A. Greenbaum and
Z. Strako\vs Predicting the behavior of finite
precision Lanczos and conjugate gradient
computations . . . . . . . . . . . . . . 121--137
Mario Arioli and
Iain Duff and
Daniel Ruiz Stopping Criteria for Iterative Solvers 138--144
Jack J. Dongarra and
Sven Hammarling and
James H. Wilkinson Numerical Considerations in Computing
Invariant Subspaces . . . . . . . . . . 145--161
Desmond J. Higham and
Nicholas J. Higham Backward Error and Condition of
Structured Linear Systems . . . . . . . 162--175
Å. Björck and
C. C. Paige Loss and Recapture of Orthogonality in
the Modified Gram--Schmidt Algorithm . . 176--190
Samuel K. Eldersveld and
Michael A. Saunders A Block-LU Update for Large-Scale Linear
Programming . . . . . . . . . . . . . . 191--201
Stanley C. Eisenstat and
Joseph W. H. Liu Exploiting Structural Symmetry in
Unsymmetric Sparse Symbolic
Factorization . . . . . . . . . . . . . 202--211
Tony F. C. Chan and
Tarek P. Mathew The Interface Probing Technique in
Domain Decomposition . . . . . . . . . . 212--238
R. O. Hill, Jr. and
B. N. Parlett Refined Interlacing Properties . . . . . 239--247
John de Pillis A Parallel Iteration Method and the
Convection-Diffusion Equation . . . . . 248--273
Daniel J. Pierce and
Robert J. Plemmons Fast Adaptive Condition Estimation . . . 274--291
Philip E. Gill and
Walter Murray and
Dulce B. Ponceleón and
Michael A. Saunders Preconditioners for Indefinite Systems
Arising in Optimization . . . . . . . . 292--311
Daniel L. Boley and
Richard P. Brent and
Gene H. Golub and
Franklin T. Luk Algorithmic Fault Tolerance Using the
Lanczos Method . . . . . . . . . . . . . 312--332
John R. Gilbert and
Cleve Moler and
Robert Schreiber Sparse Matrices in MATLAB: Design and
Implementation . . . . . . . . . . . . . 333--356
D. C. Sorensen Implicit Application of Polynomial
Filters in a $k$-step Arnoldi Method . . 357--385
P. Bjòrstad and
F. Manne and
T. Sòrevik and
M. Vajter\vsic Efficient Matrix Multiplication on SIMD
Computers . . . . . . . . . . . . . . . 386--401
Jaroslav Kautský Gauss Quadratures: An Inverse Problem 402--417
Angelika Bunse-Gerstner and
Ralph Byers and
Volker Mehrmann A Chart of Numerical Methods for
Structured Eigenvalue Problems . . . . . 419--453
I. Borosh and
L. B. Treybig A Sharp Bound on Positive Solutions of
Linear Diophantine Equations . . . . . . 454--458
Evgenij E. Tyrtyshnikov Optimal and Superoptimal Circulant
Preconditioners . . . . . . . . . . . . 459--473
H. Langer and
B. Najman and
K. Veseli\'c Perturbation of the Eigenvalues of
Quadratic Matrix Polynomials . . . . . . 474--489
Tony F. Chan and
Per Christian Hansen A look-ahead Levinson algorithm for
indefinite Toeplitz systems . . . . . . 490--506
Steve Kirkland An Eigenvalue Region for Leslie Matrices 507--529
Leiba Rodman and
Tamir Shalom On Inversion of Symmetric Toeplitz
Matrices . . . . . . . . . . . . . . . . 530--549
Ioannis I. Gerontidis Cyclic Strong Ergodicity in
Nonhomogeneous Markov Systems . . . . . 550--566
Beresford N. Parlett Reduction to Tridiagonal Form and
Minimal Realizations . . . . . . . . . . 567--593
Martin H. Gutknecht A Completed Theory of the Unsymmetric
Lanczos Process and Related Algorithms,
Part I . . . . . . . . . . . . . . . . . 594--639
Roy Mathias Matrices with Positive Definite
Hermitian Part: Inequalities and Linear
Systems . . . . . . . . . . . . . . . . 640--654
Peter Arbenz and
Gene H. Golub $ Q R $-Like Algorithms for Symmetric
Arrow Matrices . . . . . . . . . . . . . 655--658
Kurt S. Riedel A Sherman--Morrison--Woodbury Identity
for Rank Augmenting Matrices with
Application to Centering . . . . . . . . 659--662
Tony F. Chan and
Danny Goovaerts On the Relationship between Overlapping
and Nonoverlapping Domain Decomposition
Methods . . . . . . . . . . . . . . . . 663--670
Daniel B. Szyld and
Mark T. Jones Two-Stage and Multisplitting Methods for
the Parallel Solution of Linear Systems 671--679
Nicholas J. Higham Stability of a Method for Multiplying
Complex Matrices with Three Real Matrix
Multiplications . . . . . . . . . . . . 681--687
Charles Kenney and
Alan J. Laub On Scaling Newton's Method for Polar
Decomposition and the Matrix Sign
Function . . . . . . . . . . . . . . . . 688--706
Gérard Meurant A Review on the Inverse of Symmetric
Tridiagonal and Block Tridiagonal
Matrices . . . . . . . . . . . . . . . . 707--728
K. S. Arun A Unitarily Constrained Total Least
Squares Problem in Signal Processing . . 729--745
Mu Sheng Wei The Analysis for the Total Least Squares
Problem with More than One Solution . . 746--763
Thomas A. Manteuffel and
Gene H. Golub Introduction to the Special Section on
Iterative Methods in Numerical Linear
Algebra . . . . . . . . . . . . . . . . 765--766
Thomas Huckle Circulant and Skewcirculant Matrices for
Solving Toeplitz Matrix Problems . . . . 767--777
Noël M. Nachtigal and
Satish C. Reddy and
Lloyd N. Trefethen How Fast Are Nonsymmetric Matrix
Iterations? . . . . . . . . . . . . . . 778--795
Noël M. Nachtigal and
Lothar Reichel and
Lloyd N. Trefethen A Hybrid GMRES Algorithm for
Nonsymmetric Linear Systems . . . . . . 796--825
A. Greenbaum Diagonal Scalings of the Laplacian as
Preconditioners for Other Elliptic
Differential Operators . . . . . . . . . 826--846
O. Axelsson Bounds of Eigenvalues of Preconditioned
Matrices . . . . . . . . . . . . . . . . 847--862
S. Holmgren and
K. Otto Iterative Solution Methods and
Preconditioners for Block-Tridiagonal
Systems of Equations . . . . . . . . . . 863--886
Torgeir Rusten and
Ragnar Winther A Preconditioned Iterative Method for
Saddlepoint Problems . . . . . . . . . . 887--904
Stephen A. Vavasis Preconditioning for Boundary Integral
Equations . . . . . . . . . . . . . . . 905--925
Wayne Joubert Lanczos Methods for the Solution of
Nonsymmetric Systems of Linear Equations 926--943
E. F. D'Azevedo and
P. A. Forsyth and
Wei Pai Tang Ordering Methods for Preconditioned
Conjugate Gradient Methods Applied to
Unstructured Grid Problems . . . . . . . 944--961
Douglas James Implicit Nullspace Iterative Methods for
Constrained Least Squares Problems . . . 962--978
M. Eiermann and
W. Niethammer and
R. S. Varga Acceleration of Relaxation Methods for
Non-Hermitian Linear Systems . . . . . . 979--991
Bart De Moor and
Paul Van Dooren Generalizations of the Singular Value
and $ Q R $ Decompositions . . . . . . . 993--1014
Marc Moonen and
Paul Van Dooren and
Joos Vandewalle A Singular Value Decomposition Updating
Algorithm for Subspace Tracking . . . . 1015--1038
G. A. Watson Algorithms for Minimum Trace Factor
Analysis . . . . . . . . . . . . . . . . 1039--1053
G. A. Watson Computing the Structured Singular Value 1054--1066
John L. Eltinge Exponential Convergence Properties of
Autocovariance Matrix Inverses and
Latent Vector Prediction Coefficients 1067--1084
Xing Zhi Ji A Two-Dimensional Bisection Method for
Solving Two-Parameter Eigenvalue
Problems . . . . . . . . . . . . . . . . 1085--1093
J. Kuczy\'nski and
H. Wo\'zniakowski Estimating the Largest Eigenvalue by the
Power and Lanczos Algorithms with a
Random Start . . . . . . . . . . . . . . 1094--1122
Harald K. Wimmer Explicit Solutions of the Matrix
Equation $ \sum A^i X D_i = C $ . . . . 1123--1130
Richard W. Cottle and
Yow Yieh Chang Least-Index Resolution of Degeneracy In
Linear Complimentarity Problems with
Sufficient Matrices . . . . . . . . . . 1131--1141
Shmuel Friedland Inverse Eigenvalue Problems for
Symmetric Toeplitz Matrices . . . . . . 1142--1153
Wasin So Equality Cases in Matrix Exponential
Inequalities . . . . . . . . . . . . . . 1154--1158
Christopher L. Cox and
William F. Moss Backward error analysis for a pole
assignment algorithm. II. The complex
case . . . . . . . . . . . . . . . . . . 1159--1171
Hsin-Chu Chen Circulative matrices of degree $ \theta
$ . . . . . . . . . . . . . . . . . . . 1172--1188
A. Scottedward Hodel and
Kameshwar Poolla Parallel Solution of Large Lyapunov
Equations . . . . . . . . . . . . . . . 1189--1203
James Demmel and
Kre\vsimir Veseli\'c Jacobi's Method is More Accurate than $
Q R $ . . . . . . . . . . . . . . . . . 1204--1245
David S. Dodson and
Stewart A. Levin A Tricyclic Tridiagonal Equation Solver 1246--1254
H. Hu A Projective Method for Rescaling a
Diagonally Stable Matrix to be Positive
Definite . . . . . . . . . . . . . . . . 1255--1263
Gautam M. Shroff and
Christian H. Bischof Adaptive Condition Estimation for
Rank-One Updates of $ Q R $
Factorizations . . . . . . . . . . . . . 1264--1278
Jesse L. Barlow and
Udaya B. Vemulapati Rank Detection Methods for Sparse
Matrices . . . . . . . . . . . . . . . . 1279--1297
Mårten Gulliksson and
Per-Åke Wedin Modifying the $ Q R $ Decomposition to
Constrained and Weighted Linear Least
Squares . . . . . . . . . . . . . . . . 1298--1313
James W. Demmel and
Nicholas J. Higham Improved Error Bounds for
Underdetermined System Solvers . . . . . 1--14
Orna Gross and
Uriel G. Rothblum Approximations of the Spectral Radius,
Corresponding Eigenvector, and Second
Largest Modulus of an Eigenvalue for
Square, Nonnegative, Irreducible
Matrices . . . . . . . . . . . . . . . . 15--32
Chia-Chi Tsui On the Solution to Matrix Equation $ T A
- F T = L C $ and Its Applications . . . 33--44
L. Yu. Kolotilina and
A. Yu. Yeremin Factorized sparse approximate inverse
preconditionings. I. Theory . . . . . . 45--58
Z. I. Wo\'znicki Estimation of the Optimum Relaxation
Factors in Partial Factorization
Iterative Methods . . . . . . . . . . . 59--73
C. L. Frenzen and
I. Fischer On a conjecture of Pierce for permanents
of singular correlation matrices . . . . 74--81
Ji\vrí Rohn Interval Matrices: Singularity and Real
Eigenvalues . . . . . . . . . . . . . . 82--91
Miron Tismenetsky Matrix generalizations of a moment
problem theorem. I. The Hermitian case 92--112
Christopher I. Byrnes and
Xiaochang Wang The Additive Inverse Eigenvalue Problem
for Lie Perturbations . . . . . . . . . 113--117
Victor Pan Decreasing the Displacement Rank of a
Matrix . . . . . . . . . . . . . . . . . 118--121
D. Herceg and
M. M. Martins and
M. E. Trigo On the Convergence of the MSOR Method
for Some Classes of Matrices . . . . . . 122--131
Rajendra Bhatia and
Chandler Davis More Matrix Forms of the
Arithmetic-Geometric Mean Inequality . . 132--136
D. von Rosen Some Results on Homogeneous Matrix
Equations . . . . . . . . . . . . . . . 137--145
Takang Ku and
C.-C. Jay Kuo Spectral Properties of Preconditioned
Rational Toeplitz Matrices . . . . . . . 146--165
David S. Watkins Bidirectional Chasing Algorithms for the
Eigenvalue Problem . . . . . . . . . . . 166--179
Robert A. van de Geijn Deferred Shifting Schemes for Parallel $
Q R $ Methods . . . . . . . . . . . . . 180--194
Ren Cang Li Bounds on Perturbations of Generalized
Singular Values and of Associated
Subspaces . . . . . . . . . . . . . . . 195--234
Oliver Aberth and
Mark J. Schaefer Precise Matrix Eigenvalues Using Range
Arithmetic . . . . . . . . . . . . . . . 235--241
Joseph W. H. Liu and
Esmond G. Ng and
Barry W. Peyton On Finding Supernodes for Sparse Matrix
Computations . . . . . . . . . . . . . . 242--252
M. V. Bhat and
W. G. Habashi and
J. W. H. Liu and
V. N. Nguyen and
M. F. Peeters A Note on Nested Dissection for
Rectangular Grids . . . . . . . . . . . 253--258
David L. Harrar, II Orderings, Multicoloring, and
Consistently Ordered Matrices . . . . . 259--278
Beresford N. Parlett and
Jian Le Forward Instability of Tridiagonal $ Q R
$ . . . . . . . . . . . . . . . . . . . 279--316
Nicholas J. Higham Optimization by Direct Search in Matrix
Computations . . . . . . . . . . . . . . 317--333
John R. Gilbert and
Joseph W. H. Liu Elimination Structures for Unsymmetric
Sparse $ L U $ Factors . . . . . . . . . 334--352
Marc Moonen and
Paul Van Dooren and
Joos Vandewalle A Systolic Array for SVD Updating . . . 353--371
Linda Kaufman An Algorithm for the Banded Symmetric
Generalized Matrix Eigenvalue Problem 372--389
I. Olkin and
S. T. Rachev Maximum Submatrix Traces for Positive
Definite Matrices . . . . . . . . . . . 390--397
Charles R. Johnson and
Volker Mehrmann and
D. Dale Olesky Sign Controllability of a Nonnegative
Matrix and a Positive Vector . . . . . . 398--407
A. Frommer and
G. Mayer A New Criterion to Guarantee the
Feasibility of the Interval Gaussian
Algorithm . . . . . . . . . . . . . . . 408--419
Stephen Richter and
Larry D. Davis and
Emmanuel G. Collins Efficient Computation of the Solutions
to Modified Lyapunov Equations . . . . . 420--431
Min Chen and
Roger Temam Incremental Unknowns in Finite
Differences: Condition Number of the
Matrix . . . . . . . . . . . . . . . . . 432--455
L. Elsner and
I. Koltracht and
M. Neumann and
D. Xiao On Accurate Computations of the Perron
Root . . . . . . . . . . . . . . . . . . 456--467
Douglas Sweet The Use of Pivoting to Improve the
Numerical Performance of Algorithms for
Toeplitz Matrices . . . . . . . . . . . 468--493
G. W. Stewart Updating a Rank-Revealing $ U L V $
Decomposition . . . . . . . . . . . . . 494--499
Dario Bini and
Paola Favati On a Matrix Algebra Related to the
Discrete Hartley Transform . . . . . . . 500--507
Eugenius Kaszkurewicz and
Amit Bhaya Robust Stability and Diagonal Liapunov
Functions . . . . . . . . . . . . . . . 508--520
Ta-Kang Ku and
C.-C. Jay Kuo Spectral Properties of Preconditioned
Rational Toeplitz Matrices: The
Nonsymmetric Case . . . . . . . . . . . 521--544
Geir Nævdal On the Completion of Partially Given
Triangular Toeplitz Matrices to
Contractions . . . . . . . . . . . . . . 545--552
Mark T. Jones and
Merrell L. Patrick Bunch--Kaufman Factorization for Real
Symmetric Indefinite Banded Matrices . . 553--559
A. Forsgren and
W. Murray Newton Methods for Large-Scale Linear
Equality-Constrained Minimization . . . 560--587
Roy Mathias Perturbation Bounds for the Polar
Decomposition . . . . . . . . . . . . . 588--597
Jesse L. Barlow Error Analysis of Update Methods for the
Symmetric Eigenvalue Problem . . . . . . 598--618
Derek Hacon Jacobi's Method for Skew-Symmetric
Matrices . . . . . . . . . . . . . . . . 619--628
Georg Heinig and
Frank Hellinger On the Bezoutian Structure of the
Moore--Penrose Inverses of Hankel
Matrices . . . . . . . . . . . . . . . . 629--645
Pierre Comon and
Pascal Laurent-Gengoux Displacement Rank of Generalized
Inverses of Persymmetric Matrices . . . 646--654
Donovan R. Hare and
Charles R. Johnson and
D. D. Olesky and
P. van den Driessche Sparsity Analysis of the $ Q R $
Factorization . . . . . . . . . . . . . 655--669
Moshe Haviv and
Y. Ritov On Series Expansions and Stochastic
Matrices . . . . . . . . . . . . . . . . 670--676
Samprit Chatterjee and
Glenn Heller The Numerical Effect of Measurement
Error in the Explanatory Variables on
the Observed Least Squares Estimate . . 677--687
I. Gohberg and
I. Koltracht Mixed, Componentwise, and Structured
Condition Numbers . . . . . . . . . . . 688--704
Xiao Dong Zhang and
Shang Jun Yang An Improvement of Hadamard's Inequality
for Totally Nonnegative Matrices . . . . 705--711
G. O. Corrêa Necessary and Sufficient Conditions for
Bounded-Input/Bounded-State Stability of
Discrete-Time, Bilinear Systems . . . . 712--720
T. J. Suffridge and
T. L. Hayden Approximation by a Hermitian Positive
Semidefinite Toeplitz Matrix . . . . . . 721--734
Stan Cabay and
Ron Meleshko A Weakly Stable Algorithm for Padé
Approximants and the Inversion of Hankel
Matrices . . . . . . . . . . . . . . . . 735--765
Julio M. Stern and
Stephen A. Vavasis Nested Dissection for Sparse Nullspace
Bases . . . . . . . . . . . . . . . . . 766--775
A. C. M. Ran and
H. L. Trentelman Linear Quadratic Problems with
Indefinite Cost for Discrete Time
Systems . . . . . . . . . . . . . . . . 776--797
Jesse L. Barlow Error Bounds for the Computation of Null
Vectors with Applications to Markov
Chains . . . . . . . . . . . . . . . . . 798--812
Jerome Dancis Choosing the Inertias for Completions of
Certain Partially Specified Matrices . . 813--829
Man Duen Choi and
Jeffrey S. Rosenthal and
Peter Rosenthal Linear-algebraic results associated with
antiferromagnetic Heisenberg chains . . 830--852
A. Frank van der Stappen and
Rob H. Bisseling and
Johannes G. G. van de Vorst Parallel Sparse $ L U $ Decomposition on
a Mesh Network of Transputers . . . . . 853--879
Dennis S. Bernstein and
David C. Hyland Compartmental Modeling and Second-Moment
Analysis of State Space Systems . . . . 880--901
Alan L. Andrew and
K.-W. Eric Chu and
Peter Lancaster Derivatives of Eigenvalues and
Eigenvectors of Matrix Functions . . . . 903--926
Angelika Bunse-Gerstner and
Ralph Byers and
Volker Mehrmann Numerical Methods for Simultaneous
Diagonalization . . . . . . . . . . . . 927--949
Madhav P. Desai and
Vasant B. Rao On the Convergence of Reversible Markov
Chains . . . . . . . . . . . . . . . . . 950--966
V. Venkateswaran An Algorithm for the Linear
Complementarity Problem with a $ P_0
$-Matrix . . . . . . . . . . . . . . . . 967--977
R. T. Yanushevsky Robust Control of Delay Feedback Systems
with Bounded Uncertainty . . . . . . . . 978--990
K. S. Arun and
V. B. Rao Constructive Heuristics and Lower Bounds
for Graph Partitioning Based on a
Principal-Components Approximation . . . 991--1015
Debajyoti Pal and
Thomas Kailath Fast Triangular Factorization and
Inversion of Hermitian, Toeplitz, and
Related Matrices with Arbitrary Rank
Profile . . . . . . . . . . . . . . . . 1016--1042
Charles R. Johnson and
Peter M. Nylen Length Bounds for Singular Values of
Sparse Matrices . . . . . . . . . . . . 1043--1047
Panos M. Pardalos and
Yinyu Ye and
Chi-Geun Han and
John A. Kaliski Solution of $ P_0 $-Matrix Linear
Complementarity Problems Using a
Potential Reduction Algorithm . . . . . 1048--1060
Roy Mathias Approximation of Matrix-Valued Functions 1061--1063
S. E. Leurgans and
R. T. Ross and
R. B. Abel A Decomposition for Three-Way Arrays . . 1064--1083
Natália Bebiano and
Chi-Kwong Li and
João da Providência Some Results on the Numerical Range of a
Derivation . . . . . . . . . . . . . . . 1084--1095
Rajiv Vijayan and
H. Vincent Poor Fast Triangular Factorization of
Covariance Matrices of Differenced Time
Series . . . . . . . . . . . . . . . . . 1096--1102
Kazuo Murota On the Smith Normal Form of Structured
Polynomial Matrices, II . . . . . . . . 1103--1111
Guo Dong Zhang On the Sensitivity of the Solution of
Nearly Uncoupled Markov Chains . . . . . 1112--1123
Hong Yuan Zha A Componentwise Perturbation Analysis of
the $ Q R $ Decomposition . . . . . . . 1124--1131
M. Gasca and
J. M. Peña Total Positivity, $ Q R $ Factorization,
and Neville Elimination . . . . . . . . 1132--1140
G. W. Stewart On the Perturbation of $ L U $,
Cholesky, and $ Q R $ Factorizations . . 1141--1145
Randolph P. Flowe and
Gary A. Harris A Note on Generalized Vandermonde
Determinants . . . . . . . . . . . . . . 1146--1151
Roy Mathias The Hadamard Operator Norm of a
Circulant and Applications . . . . . . . 1152--1167
Bintong Chen and
Patrick T. Harker A Non-Interior-Point Continuation Method
for Linear Complementarity Problems . . 1168--1190
Tony F. Chan and
Per Christian Hansen Erratum: ``A look-ahead Levinson
algorithm for indefinite Toeplitz
systems'' [SIAM J. Matrix Anal. Appl.
\bf 13 (1992), no. 2, 490--506 and MR
93a:65032] . . . . . . . . . . . . . . . 1191--1191
Uriel G. Rothblum and
Hans Schneider and
Michael H. Schneider Scaling Matrices to Prescribed Row and
Column Maxima . . . . . . . . . . . . . 1--14
Martin H. Gutknecht A Completed Theory of the Unsymmetric
Lanczos Process and Related Algorithms,
Part II . . . . . . . . . . . . . . . . 15--58
C.-T. Pan and
Kermit Sigmon A Bottom-Up Inductive Proof of the
Singular Value Decomposition . . . . . . 59--61
John R. Gilbert Predicting Structure in Sparse Matrix
Computations . . . . . . . . . . . . . . 62--79
Raymond H. Chan and
James G. Nagy and
Robert J. Plemmons Circulant Preconditioned Toeplitz Least
Squares Iterations . . . . . . . . . . . 80--97
Servet Martínez and
Gérard Michon and
Jaime San Martín Inverse of Strictly Ultrametric Matrices
are of Stieltjes Type . . . . . . . . . 98--106
Reinhard Nabben and
Richard S. Varga A Linear Algebra Proof that the Inverse
of a Strictly Ultrametric Matrix Is a
Strictly Diagonally Dominant Stieltjes
Matrix . . . . . . . . . . . . . . . . . 107--113
T. Kailath and
J. Chun Generalized Displacement Structure for
Block-Toeplitz, Toeplitz-Block, and
Toeplitz-Derived Matrices . . . . . . . 114--128
David Carlson On the Controllability of Matrix Pairs
($A$, $K$) with $K$ Positive
Semidefinite, II . . . . . . . . . . . . 129--133
Stephen Barnett Reduction of a Transfer Function via an
Observability Matrix . . . . . . . . . . 134--139
Reuven Ackner and
Hanoch Lev-Ari and
Thomas Kailath The Schur Algorithm for Matrix-Valued
Meromorphic Functions . . . . . . . . . 140--150
Kai Sheng Lu and
Jia Ning Wei Reducibility Condition of a Class of
Rational Function Matrices . . . . . . . 151--161
Andrew A. Anda and
Haesun Park Fast Plane Rotations with Dynamic
Scaling . . . . . . . . . . . . . . . . 162--174
Ji\vrí Rohn Positive Definiteness and Stability of
Interval Matrices . . . . . . . . . . . 175--184
Haesun Park ESPRIT Direction-of-Arrival Estimation
in the Presence of Spatially Correlated
Noise . . . . . . . . . . . . . . . . . 185--193
Alan H. Feiveson Finding the Best Regression Subset by
Reduction in Nonfull-Rank Cases . . . . 194--204
Susan L. Handy and
Jesse L. Barlow Numerical Solution of the Eigenproblem
for Banded, Symmetric Toeplitz Matrices 205--214
Walter F. Mascarenhas A Note on Jacobi Being More Accurate
Than $ Q R $ . . . . . . . . . . . . . . 215--218
Donald W. Fausett and
Charles T. Fulton Large Least Squares Problems Involving
Kronecker Products . . . . . . . . . . . 219--227
Roger G. Grimes and
John G. Lewis and
Horst D. Simon A Shifted Block Lanczos Algorithm for
Solving Sparse Symmetric Generalized
Eigenproblems . . . . . . . . . . . . . 228--272
Mark T. Jones and
Merrell L. Patrick Factoring symmetric indefinite matrices
on high-performance architectures . . . 273--283
R. V. Patel and
Z. Lin and
P. Misra Computation of Stable Invariant
Subspaces of Hamiltonian Matrices . . . 284--298
J. William Helton and
Daniel Lam and
Hugo J. Woerdeman Sparsity Patterns with High Rank
Extremal Positive Semidefinite Matrices 299--312
Carl C. Cowen and
Michael A. Dritschel and
Richard C. Penney Norms of Hadamard Multipliers . . . . . 313--320
S. Bondeli and
W. Gander Cyclic Reduction for Special Tridiagonal
Systems . . . . . . . . . . . . . . . . 321--330
Ping Tak Peter Tang Dynamic Condition Estimation and
Rayleigh--Ritz Approximation . . . . . . 331--346
Bart De Moor On the Structure of Generalized Singular
Value and $ Q R $ Decompositions . . . . 347--358
Richard A. Brualdi and
Bryan L. Shader Strong Hall Matrices . . . . . . . . . . 359--365
Gary E. Adams and
Adam W. Boja\'nczyk and
Franklin T. Luk Computing the PSVD of Two $ 2 \times 2 $
Triangular Matrices . . . . . . . . . . 366--382
M. M. Konstantinov and
P. Hr. Petkov and
N. D. Christov Nonlocal Perturbation Analysis of the
Schur System of a Matrix . . . . . . . . 383--392
Rafael Brú and
José Mas and
Ana M. Urbano An Algorithm for the Single-Input Pole
Assignment Problem . . . . . . . . . . . 393--407
J. M. Varah Backward Error Estimates for Toeplitz
Systems . . . . . . . . . . . . . . . . 408--417
Georg Heinig and
Frank Hellinger Moore--Penrose Inversion of Square
Toeplitz Matrices . . . . . . . . . . . 418--450
Debajyoti Pal and
Thomas Kailath Fast Triangular Factorization and
Inversion of Hankel and Related Matrices
with Arbitrary Rank Profile . . . . . . 451--478
Thomas Huckle The Arnoldi Method for Normal Matrices 479--489
Louis de Mesnard Unicity of Biproportion . . . . . . . . 490--495
David Colella and
Christopher Heil Characterizations of Scaling Functions:
Continuous Solutions . . . . . . . . . . 496--518
Roger A. Horn and
Chi-Kwong Li and
Dennis I. Merino Linear Operators Preserving Complex
Orthogonal Equivalence on Matrices . . . 519--529
E. R. Jessup and
D. C. Sorensen A Parallel Algorithm for Computing the
Singular Value Decomposition of a Matrix 530--548
Å. Björck and
H. Park and
L. Eldén Accurate Downdating of Least Squares
Solutions . . . . . . . . . . . . . . . 549--568
M. Hanke Iterative Consistency: a Concept for the
Solution of Singular Systems of Linear
Equations . . . . . . . . . . . . . . . 569--577
Michael Neumann and
Hans Schneider Algorithms for Computing Bases for the
Perron Eigenspace with Prescribed
Nonnegativity and Combinational
Properties . . . . . . . . . . . . . . . 578--591
Shivkumar Chandrasekaran and
Ilse C. F. Ipsen On Rank-Revealing Factorisations . . . . 592--622
Moody T. Chu and
Melissa A. Erbrecht Symmetric Toeplitz Matrices with Two
Prescribed Eigenpairs . . . . . . . . . 623--635
Zhi-Quan Luo and
Paul Tseng Perturbation Analysis of a Condition
Number for Linear Systems . . . . . . . 636--660
Richard J. Vaccaro A Second-Order Perturbation Expansion
for the SVD . . . . . . . . . . . . . . 661--671
J. Kuczy\'nski and
H. Wo\'zniakowski Probabilistic Bounds on the Extremal
Eigenvalues and Condition Number by the
Lanczos Algorithm . . . . . . . . . . . 672--691
Nai Kuan Tsao An error model for Swarztrauber's
parallel tridiagonal equation solver . . 692--713
Carl D. Meyer Sensitivity of the Stationary
Distribution of a Markov Chain . . . . . 715--728
Abraham Berman and
Dafna Shasha Strongly Inertia-Preserving Matrices . . 729--732
U. Helmke and
J. B. Moore and
J. E. Perkins Dynamical Systems that Compute Balanced
Realizations and the Singular Value
Decomposition . . . . . . . . . . . . . 733--754
Ronald J. Stern and
Henry Wolkowicz Trust Region Problems and Nonsymmetric
Eigenvalue Perturbations . . . . . . . . 755--778
M. Seetharama Gowda and
Roman Sznajder The Generalized Order Linear
Complementarity Problem . . . . . . . . 779--795
Carolyn Pillers Dobler A Matrix Approach to Finding a Set of
Generators and Finding the Polar (Dual)
of a Class of Polyhedral Cones . . . . . 796--803
Bernhard Beckermann and
George Labahn A Uniform Approach for the Fast
Computation of Matrix-type Padé
Approximants . . . . . . . . . . . . . . 804--823
A. I. Ze\vcevi\'c and
D. D. \vSiljak A Block-Parallel Newton Method via
Overlapping Epsilon Decompositions . . . 824--844
A. C. M. Ran and
L. Rodman Factorization of Matrix Polynomials with
Symmetries . . . . . . . . . . . . . . . 845--864
V. L. Syrmos and
F. L. Lewis Decomposability and Quotient Subspaces
for the Pencil $ s L - M $ . . . . . . . 865--880
J. B. Moore and
R. E. Mahony and
U. Helmke Numerical Gradient Algorithms for
Eigenvalue and Singular Value
Calculations . . . . . . . . . . . . . . 881--902
Chi-Kwong Li and
Bit Shun Tam A Note on Extreme Correlation Matrices 903--908
Alison Ramage and
Andrew J. Wathen On Preconditioning for Finite Element
Equations on Irregular Grids . . . . . . 909--921
C. Brezinski and
M. Morandi Cecchi and
M. Redivo-Zaglia The Reverse Bordering Method . . . . . . 922--937
William F. Trench Some Spectral Properties of Hermitian
Toeplitz Matrices . . . . . . . . . . . 938--942
David Watkins and
Ludwig Elsner Theory of Decomposition and
Bulge-Chasing Algorithms for the
Generalized Eigenvalue Problem . . . . . 943--967
Robert C. Thompson The Diagonal Torus of a Matrix under
Special Unitary Equivalence . . . . . . 968--973
Guanghan Xu and
Thomas Kailath Fast Estimation of Principal Eigenspace
Using Lanczos Algorithm . . . . . . . . 974--994
Walter D. Morris, Jr. LCP Degree Theory and Oriented Matroids 995--1006
Rajendra Bhatia and
Kalyan Mukherjea Variation of the Unitary Part of a
Matrix . . . . . . . . . . . . . . . . . 1007--1014
Shmuel Friedland and
Leonid Gurvits An Upper Bound for the Real Part of
Nonmaximal Eigenvalues of Nonnegative
Irreducible Matrices . . . . . . . . . . 1015--1017
L. Eldén and
H. Park Block Downdating of Least Squares
Solutions . . . . . . . . . . . . . . . 1018--1034
Lajos László An Attainable Lower Bound for the Best
Normal Approximation . . . . . . . . . . 1035--1043
Bo Kågström A Perturbation Analysis of the
Generalized Sylvester Equation $ (A R -
L B, D R - L E) = (C, F) $ . . . . . . . 1045--1060
Ilse C. F. Ipsen and
Carl D. Meyer Uniform Stability of Markov Chains . . . 1061--1074
John R. Gilbert and
Esmond G. Ng and
Barry W. Peyton An Efficient Algorithm to Compute Row
and Column Counts for Sparse Cholesky
Factorization . . . . . . . . . . . . . 1075--1091
Stephen J. Kirkland and
Michael Neumann Convexity and concavity of the Perron
root and vector of Leslie matrices with
applications to a population model . . . 1092--1107
Stephen A. Vavasis Stable Numerical Algorithms for
Equilibrium Systems . . . . . . . . . . 1108--1131
David P. Stanford and
José Miguel Urbano Some Convergence Properties of Matrix
Sets . . . . . . . . . . . . . . . . . . 1132--1140
Jean-Pierre A. Haeberly and
Michael L. Overton A Hybrid Algorithm for Optimizing
Eigenvalues of Symmetric Definite
Pencils . . . . . . . . . . . . . . . . 1141--1156
Shmuel Friedland and
Rohan Hemasinha and
Hans Schneider and
Jeffrey Stuart and
James Weaver Row Sums and Inverse Row Sums for
Nonnegative Matrices . . . . . . . . . . 1157--1166
Ricardo D. Fierro and
James R. Bunch Collinearity and Total Least Squares . . 1167--1181
M. A. Wicks and
R. A. DeCarlo Rank Robustness of Complex Matrices with
Respect to Real Perturbations . . . . . 1182--1207
Thomas H. Robey and
Deborah L. Sulsky Row Ordering for a Sparse $ Q R $
Decomposition . . . . . . . . . . . . . 1208--1225
Hisashi Ito and
Satoru Iwata and
Kazuo Murota Block-Triangularizations of Partitioned
Matrices under Similarity/Equivalence
Transformations . . . . . . . . . . . . 1226--1255
Chi-Kwong Li and
Leiba Rodman Numerical Range of Matrix Polynomials 1256--1265
Ming Gu and
Stanley C. Eisenstat A Stable and Efficient Algorithm for the
Rank-One Modification of the Symmetric
Eigenproblem . . . . . . . . . . . . . . 1266--1276
Hao Lu Fast Solution of Confluent Vandermonde
Linear Systems . . . . . . . . . . . . . 1277--1289
I. Gohberg and
I. Koltracht and
D. Xiao Condition and Accuracy of Algorithms for
Computing Schur Coefficients of Toeplitz
Matrices . . . . . . . . . . . . . . . . 1290--1309
K. A. Cliffe and
T. J. Garratt and
A. Spence Eigenvalues of Block Matrices Arising
from Problems in Fluid Mechanics . . . . 1310--1318
Zlatko Drma\vc and
Matja\vz Omladi\vc and
Kre\vsimir Veseli\'c On the Perturbation of the Cholesky
Factorization . . . . . . . . . . . . . 1319--1332
Loyce Adams and
Peter Arbenz Towards a Divide and Conquer Algorithm
for the Real Nonsymmetric Eigenvalue
Problem . . . . . . . . . . . . . . . . 1333--1353
Leslie V. Foster Gaussian Elimination with Partial
Pivoting Can Fail in Practice . . . . . 1354--1362
Ian A. Cavers A Hybrid Tridiagonalization Algorithm
for Symmetric Sparse Matrices . . . . . 1363--1380
Richard A. Brualdi and
Shmuel Friedland and
Alex Pothen The Sparse Basis Problem and Multilinear
Algebra . . . . . . . . . . . . . . . . 1--20
Vaidyanath Mani and
Robert E. Hartwig Duality and black box interpolation. I.
The one variable nonderogatory case . . 21--28
V. Balakrishnan and
S. Boyd Existence and Uniqueness of Optimal
Matrix Scalings . . . . . . . . . . . . 29--39
A. W. Bojanczyk and
R. P. Brent and
F. R. De Hoog and
D. R. Sweet On the stability of the Bareiss and
related Toeplitz factorization
algorithms . . . . . . . . . . . . . . . 40--57
Tiberiu Constantinescu and
Ali H. Sayed and
Thomas Kailath Displacement Structure and Completion
Problems . . . . . . . . . . . . . . . . 58--78
Ming Gu and
Stanley C. Eisenstat A Divide-and-Conquer Algorithm for the
Bidiagonal SVD . . . . . . . . . . . . . 79--92
S. Chandrasekaran and
I. C. F. Ipsen On the Sensitivity of Solution
Components in Linear Systems of
Equations . . . . . . . . . . . . . . . 93--112
Werner Kratz An Index Theorem for Monotone
Matrix-Valued Functions . . . . . . . . 113--122
M. A. Wicks and
R. A. DeCarlo Computing Most Nearly Rank-Reducing
Structured Matrix Perturbations . . . . 123--137
Haesun Park and
Lars Eldén Downdating the Rank-Revealing URV
Decomposition . . . . . . . . . . . . . 138--155
Marlis Hochbruck and
Gerhard Starke Preconditioned Krylov Subspace Methods
for Lyapunov Matrix Equations . . . . . 156--171
Ming Gu and
Stanley C. Eisenstat A divide-and-conquer algorithm for the
symmetric tridiagonal eigenproblem . . . 172--191
Howard C. Elman and
Xuejun Zhang Algebraic Analysis of the Hierarchical
Basis Preconditioner . . . . . . . . . . 192--206
Moody T. Chu Constructing a Hermitian Matrix from Its
Diagonal Entries and Eigenvalues . . . . 207--217
J. N. Lyness and
P. Keast Application of the Smith Normal Form to
the Structure of Lattice Rules . . . . . 218--231
K. Zi\ketak Strict Approximation of Matrices . . . . 232--234
Michael T. Heath and
Padma Raghavan A Cartesian Parallel Nested Dissection
Algorithm . . . . . . . . . . . . . . . 235--253
Yu-Ling Lai and
Apostolos Hadjidimos and
Elias N. Houstis and
John R. Rice On the Iterative Solution of Hermite
Collocation Equations . . . . . . . . . 254--277
Leiba Rodman and
Hugo J. Woerdeman Perturbations, Singular Values, and
Ranks of Partial Triangular Matrices . . 278--288
Vassilis Syrmos and
Petr Zagalak and
Vladimír Ku\vcera External Descriptions and Staircase
Forms in Implicit Systems . . . . . . . 289--306
Geoff A. Latham A Remark on Minc's Maximal Eigenvector
Bound for Positive Matrices . . . . . . 307--311
Enrico Bozzo and
Carmine Di Fiore On the Use of Certain Matrix Algebras
Associated with Discrete Trigonometric
Transforms in Matrix Displacement
Decomposition . . . . . . . . . . . . . 312--326
Ren Cang Li New Perturbation Bounds for the Unitary
Polar Factor . . . . . . . . . . . . . . 327--332
Fuad Kittaneh Singular Values of Companion Matrices
and Bounds on Zeros of Polynomials . . . 333--340
Nicholas J. Higham and
Philip A. Knight Matrix Powers in Finite Precision
Arithmetic . . . . . . . . . . . . . . . 343--358
O. L. Mangasarian and
J. S. Pang The Extended Linear Complementarity
Problem . . . . . . . . . . . . . . . . 359--368
Mihály Bakonyi and
Hugo J. Woerdeman Maximum Entropy Elements in the
Intersection of an Affine Space and the
Cone of Positive Definite Matrices . . . 369--376
A. George and
K. Ikramov and
A. N. Krivoshapova and
W.-P. Tang A Finite Procedure for the
Tridiagonalization of a General Matrix 377--387
Ali H. Sayed and
Thomas Kailath A Look-Ahead Block Schur Algorithm for
Toeplitz-like Matrices . . . . . . . . . 388--414
Ji\vrí Rohn and
Vladik Kreinovich Computing Exact Componentwise Bounds on
Solutions of Linear Systems with
Interval Data is NP-Hard . . . . . . . . 415--420
Niloufer Mackey Hamilton and Jacobi Meet Again:
Quaternions and the Eigenvalue Problem 421--435
Rafael Bru and
Joan Josep Climent and
Michael Neumann On the Index of Block Upper Triangular
Matrices . . . . . . . . . . . . . . . . 436--447
Fred B. Weissler Some Remarks Concerning Iterative
Methods for Linear Systems . . . . . . . 448--461
Steven L. Lee A Practical Upper Bound for Departure
from Normality . . . . . . . . . . . . . 462--468
David S. Watkins Forward Stability and Transmission of
Shifts in the $ Q R $ Algorithm . . . . 469--487
Kenneth R. Driessel and
Wasin So Linear operators on matrices: preserving
spectrum and displacement structure . . 488--501
Peter Niels Heller Rank $M$ Wavelets with $N$ Vanishing
Moments . . . . . . . . . . . . . . . . 502--519
S. Chandrasekaran and
I. C. F. Ipsen Analysis of a $ Q R $ Algorithm for
Computing Singular Values . . . . . . . 520--535
Phillip A. Regalia and
François Desbouvries Displacement Structures of Covariance
Matrices, Lossless Systems, and
Numerical Algorithm Design . . . . . . . 536--564
Roy Mathias Condition Estimation for Matrix
Functions via the Schur Decomposition 565--578
Huixia Zhu and
Gerhard X. Ritter The $p$-Product and Its Applications in
Signal Processing . . . . . . . . . . . 579--601
Imad M. Jaimoukha and
Ebrahim M. Kasenally Oblique Projection Methods for Large
Scale Model Reduction . . . . . . . . . 602--627
E. Boman and
I. Koltracht Fast Transform Based Preconditioners for
Toeplitz Equations . . . . . . . . . . . 628--645
Mihály Bakonyi and
Charles R. Johnson The Euclidean distance matrix completion
problem . . . . . . . . . . . . . . . . 646--654
Hao Lu Fast Algorithms for Confluent
Vandermonde Linear Systems and
Generalized Trummer's Problem . . . . . 655--674
Mårten Gulliksson Backward Error Analysis for the
Constrained and Weighted Linear Least
Squares Problem When Using the Weighted
$ Q R $ Factorization . . . . . . . . . 675--687
Osman Güler and
Alan J. Hoffman and
Uriel G. Rothblum Approximations to Solutions to Systems
of Linear Inequalities . . . . . . . . . 688--696
Michael L. Overton and
Robert S. Womersley Second Derivatives for Optimizing
Eigenvalues of Symmetric Matrices . . . 697--718
Satoru Iwata and
Kazuo Murota A minimax theorem and a
Dulmage--Mendelsohn type decomposition
for a class of generic partitioned
matrices . . . . . . . . . . . . . . . . 719--734
Miroslav Fiedler On a Special Class of Generalized Doubly
Stochastic Matrices and Its Relation to
Bézier Polygons . . . . . . . . . . . . . 735--742
Ricardo D. Fierro and
James R. Bunch Bounding the Subspaces from Rank
Revealing Two-Sided Orthogonal
Decompositions . . . . . . . . . . . . . 743--759
Ji Guang Sun Perturbation Analysis of the Cholesky
Downdating and $ Q R $ Updating Problems 760--775
T. Gudmundsson and
C. S. Kenney and
A. J. Laub Small-Sample Statistical Estimates for
Matrix Norms . . . . . . . . . . . . . . 776--792
Ming Gu and
Stanley C. Eisenstat Downdating the Singular Value
Decomposition . . . . . . . . . . . . . 793--810
Petre Stoica and
Anders Eriksson and
Torsten Söderström Optimally Weighted MUSIC for Frequency
Estimation . . . . . . . . . . . . . . . 811--827
Thomas Lundy and
Asok K. Sen Sign Pattern Analysis of Control
Coefficients of Metabolic Pathways . . . 828--842
Zhong Xiao Jia The Convergence of Generalized Lanczos
Methods for Large Unsymmetric
Eigenproblems . . . . . . . . . . . . . 843--862
Adhemar Bultheel and
Marc Van Barel Vector Orthogonal Polynomials and Least
Squares Approximation . . . . . . . . . 863--885
Leonid Faybusovich On a Matrix Generalization of
Affine-Scaling Vector Fields . . . . . . 886--897
Hans Joachim Schmid Two-Dimensional Minimal Cubature
Formulas and Matrix Equations . . . . . 898--921
Jacob van der Woude and
Kazuo Murota Disturbance Decoupling with Pole
Placement for Structured Systems: a
Graph-Theoretic Approach . . . . . . . . 922--942
Geoff A. Latham Existence of EMS Solutions and A Priori
Estimates . . . . . . . . . . . . . . . 943--953
Daniel P. Heyman Accurate Computation of the Fundamental
Matrix of a Markov Chain . . . . . . . . 954--963
R. B. Bapat and
David P. Stanford and
P. van den Driessche Pattern Properties and Spectral
Inequalities in Max Algebra . . . . . . 964--976
Roy Mathias Accurate Eigensystem Computations by
Jacobi Methods . . . . . . . . . . . . . 977--1003
Charles R. Johnson and
Brenda K. Kroschel Principal Submatrices, Geometric
Multiplicities, and Structured
Eigenvectors . . . . . . . . . . . . . . 1004--1012
Shu-An Hu and
Ronald L. Smith The Schur Complement Interlacing Theorem 1013--1023
M. I. Gillespie and
D. D. Olesky Ordering Givens Rotations for Sparse $ Q
R $ Factorization . . . . . . . . . . . 1024--1041
Angelika Bunse-Gerstner and
Chun Yang He On a Sturm Sequence of Polynomials for
Unitary Hessenberg Matrices . . . . . . 1043--1055
Bryan L. Shader Least Squares Sign-Solvability . . . . . 1056--1073
O. Axelsson and
H. Lu On Eigenvalue Estimates for Block
Incomplete Factorization Methods . . . . 1074--1085
Chris H. Walshaw Diagonal Dominance in the Parallel
Partition Method for Tridiagonal Systems 1086--1099
J. M. Peña Matrices with Sign Consistency of a
Given Order . . . . . . . . . . . . . . 1100--1106
A. George and
Kh. D. Ikramov and
E. V. Matushkina and
W.-P. Tang On a $ Q R $-like algorithm for some
structured eigenvalue problems . . . . . 1107--1126
Steve Kirkland The Group Inverse Associated with an
Irreducible Periodic Nonnegative Matrix 1127--1134
A. A. Nikishin and
A. Yu Yeremin Variable Block CG Algorithms for Solving
Large Sparse Symmetric Positive Definite
Linear Systems on Parallel Computers, I:
General Iterative Scheme . . . . . . . . 1135--1153
Ronald B. Morgan A Restarted GMRES Method Augmented with
Eigenvectors . . . . . . . . . . . . . . 1154--1171
Hong Yuan Zha Comments on: ``Large least squares
problems involving Kronecker products''
[SIAM J. Matrix. Anal. Appl. \bf 15
(1994), no. 1, 219--227 and MR
95d:65024] by D. W. Fausett and C. T.
Fulton . . . . . . . . . . . . . . . . . 1172--1172
Bo Ying Wang and
Fu Zhen Zhang Trace and Eigenvalue Inequalities for
Ordinary and Hadamard Products of
Positive Semidefinite Hermitian Matrices 1173--1183
Xiaobai Sun and
Christian Bischof A Basis-Kernel Representation of
Orthogonal Matrices . . . . . . . . . . 1184--1196
Walter F. Mascarenhas On the Convergence of the Jacobi Method
for Arbitrary Orderings . . . . . . . . 1197--1209
R. Bru and
C. Corral and
A. Martínez and
J. Mas Multisplitting Preconditioners Based on
Incomplete Choleski Factorizations . . . 1210--1222
Götz Alefeld and
Günter Mayer On the Symmetric and Unsymmetric
Solution Set of Interval Systems . . . . 1223--1240
Lina Hemmingsson A Domain Decomposition Method for
First-Order PDEs . . . . . . . . . . . . 1241--1267
G. S. R. Murthy and
T. Parthasarathy Some Properties of Fully Semimonotone $
Q0 $-Matrices . . . . . . . . . . . . . 1268--1286
Stephen J. Wright Stability of Linear Equations Solvers in
Interior-Point Methods . . . . . . . . . 1287--1307
Carsten W. Scherer The algebraic Riccati equation and
inequality for systems with
uncontrollable modes on the imaginary
axis . . . . . . . . . . . . . . . . . . 1308--1327
Ji Guang Sun Perturbation Bounds for the Generalized
Schur Decomposition . . . . . . . . . . 1328--1340
Avram Sidi Application of Vector-Valued Rational
Approximations to the Matrix Eigenvalue
Problem and Connections with Krylov
Subspace Methods . . . . . . . . . . . . 1341--1369
Erik Elmroth and
Bo Kågström The Set of $2$-by-$3$ Matrix Pencils ---
Kronecker Structures and Their
Transitions Under Perturbations . . . . 1--34
Philip E. Gill and
Michael A. Saunders and
Joseph R. Shinnerl On the Stability of Cholesky
Factorization for Symmetric
Quasidefinite Systems . . . . . . . . . 35--46
Stephen G. Nash and
Ariela Sofer Preconditioning Reduced Matrices . . . . 47--68
Ji-guang Sun Residual Bounds on Approximate Solutions
for the Unitary Eigenproblem . . . . . . 69--82
Jane K. Cullum and
Ralph A. Willoughby A $ Q L $ Procedure for Computing the
Eigenvalues of Complex Symmetric
Tridiagonal Matrices . . . . . . . . . . 83--109
J. Ben Rosen and
Haesun Park and
John Glick Total Least Norm Formulation and
Solution for Structured Problems . . . . 110--126
Hao Lu Solution of Vandermonde-like Systems and
Confluent Vandermonde-like Systems . . . 127--138
Alle-Jan van der Veen A Schur Method for Low-Rank Matrix
Approximation . . . . . . . . . . . . . 139--160
Jean-François Cardoso and
Antoine Souloumiac Jacobi Angles for Simultaneous
Diagonalization . . . . . . . . . . . . 161--164
D. Calvetti and
L. Reichel Application of ADI Iterative Methods to
the Restoration of Noisy Images . . . . 165--186
Anders Forsgren and
Philip E. Gill and
Joseph R. Shinnerl Stability of symmetric ill-conditioned
systems arising in interior methods for
constrained optimization . . . . . . . . 187--211
Ali R. Ghavimi and
Alan J. Laub Numerical methods for nearly singular
constrained matrix Sylvester equations 212--221
Jane Cullum and
Anne Greenbaum Relations Between Galerkin and
Norm-Minimizing Iterative Methods for
Solving Linear Systems . . . . . . . . . 223--247
Stan Cabay and
Anthony R. Jones and
George Labahn Computation of numerical Padé--Hermite
and simultaneous Padé systems. I. Near
inversion of generalized Sylvester
matrices . . . . . . . . . . . . . . . . 248--267
Stan Cabay and
Anthony R. Jones and
George Labahn Computation of numerical Padé--Hermite
and simultaneous Padé systems. II. A
weakly stable algorithm . . . . . . . . 268--297
P. N. Shivakumar and
Joseph J. Williams and
Qiang Ye and
Corneliu A. Marinov On Two-Sided Bounds Related to Weakly
Diagonally Dominant $M$-Matrices With
Application to Digital Circuit Dynamics 298--312
Ji-Guang Sun Perturbation Analysis of the Pole
Assignment Problem . . . . . . . . . . . 313--331
Michel Verhaegen A Subspace Model Identification Solution
to the Identification of Mixed Causal,
Anti-Causal $ L T I $ Systems . . . . . 332--347
Alan George and
Kh. Ikramov Is the Polar Decomposition Finitely
Computable? . . . . . . . . . . . . . . 348--354
J.-P. Le Cadre On the Properties of a Relative Entropy
Functional . . . . . . . . . . . . . . . 355--382
Ricardo D. Fierro Perturbation Analysis for Two-Sided (or
Complete) Orthogonal Decompositions . . 383--400
Gerard L. G. Sleijpen and
Henk A. van der Vorst A Jacobi--Davidson Iteration Method for
Linear Eigenvalue Problems . . . . . . . 401--425
Peter Kunkel and
Volker Mehrmann Generalized Inverses of
Differential-Algebraic Operators . . . . 426--442
Esmond G. Ng and
Barry W. Peyton Some Results on Structure Prediction in
Sparse $ Q R $ Factorization . . . . . . 443--459
Charles R. Johnson In memoriam: Robert C. Thompson
(1931--1995) . . . . . . . . . . . . . . 463--464
Anne Greenbaum and
Vlastimil Pták and
Zden\vek Strako\vs Any Nonincreasing Convergence Curve Is
Possible for GMRES . . . . . . . . . . . 465--469
Dianne P. O'Leary and
Yuan-Jye Jason Wu A Block-GTH Algorithm for Finding the
Stationary Vector of a Markov Chain . . 470--488
Richard A. Brualdi and
Suk-Geun Hwang On the spectral radius of $ (0,
1)$-matrices with $1$'s in prescribed
positions . . . . . . . . . . . . . . . 489--508
Zlatko Drma\vc On the Condition Behaviour in the Jacobi
Method . . . . . . . . . . . . . . . . . 509--514
Dimitrios Noutsos An Operator Relation of the USSOR and
the Jacobi Iteration Matrices of a
$p$-Cyclic Matrix . . . . . . . . . . . 515--529
Monique Laurent and
Svatopluk Poljak On the Facial Structure of the Set of
Correlation Matrices . . . . . . . . . . 530--547
Ilan Bar-On Interlacing Properties of Tridiagonal
Symmetric Matrices with Applications to
Parallel Computing . . . . . . . . . . . 548--562
M. Radjabalipour and
A. Salemi On Eigenvalues of Quadratic Matrix
Polynomials and Their Perturbations . . 563--569
Luca Dieci and
Benedetta Morini and
Alessandra Papini Computational Techniques for Real
Logarithms of Matrices . . . . . . . . . 570--593
M. Seetharama Gowda An Analysis of Zero Set and Global Error
Bound Properties of a Piecewise Affine
Function Via Its Recession Function . . 594--609
Roy Mathias A Chain Rule for Matrix Functions and
Applications . . . . . . . . . . . . . . 610--620
Dao-Sheng Zheng Further Study and Generalization of
Kahan's Matrix Extension Theorem . . . . 621--631
Shu-fang Xu On the Jacobi Matrix Inverse Eigenvalue
Problem with Mixed Given Data . . . . . 632--639
Paola Sebastiani On the Derivatives of Matrix Powers . . 640--648
Sanjay P. Bhat and
Dennis S. Bernstein Second-Order Systems with Singular Mass
Matrix and an Extension of Guyan
Reduction . . . . . . . . . . . . . . . 649--657
Szu-Min Lu and
Jesse L. Barlow Multifrontal Computation with the
Orthogonal Factors of Sparse Matrices 658--679
A. George and
Kh. Ikramov and
W.-P. Tang and
V. N. Tchugunov On Doubly Symmetric Tridiagonal Forms
for Complex Matrices and Tridiagonal
Inverse Eigenvalue Problems . . . . . . 680--690
Daniel Hershkowitz Uniqueness of Sum Decompositions of
Symmetric Matrices . . . . . . . . . . . 691--705
V. Faber and
W. Joubert and
E. Knill and
T. Manteuffel Minimal Residual Method Stronger than
Polynomial Preconditioning . . . . . . . 707--729
M. A. Goberna and
M. A. Lopez and
M. Todorov Stability Theory for Linear Inequality
Systems . . . . . . . . . . . . . . . . 730--743
Yimin Wei A Characterization and Representation of
the Drazin Inverse . . . . . . . . . . . 744--747
Jungong Xue Computing the Smallest Eigenvalue of an
$M$-Matrix . . . . . . . . . . . . . . . 748--762
Anders Forsgren On Linear Least-Squares Problems with
Diagonally Dominant Weight Matrices . . 763--788
R. B. Lehoucq and
D. C. Sorensen Deflation Techniques for an Implicitly
Restarted Arnoldi Iteration . . . . . . 789--821
Marc Artzrouni On the Dynamics of the Linear Process $
Y(k) = A(k) Y(k - 1) $ with Irreducible
Matrices $ A(k) $ . . . . . . . . . . . 822--833
S. K. Jain and
S. K. Mitra and
H. J. Werner Extensions of $ {\cal {G}}$-based matrix
partial orders . . . . . . . . . . . . . 834--850
Christian Kanzow Some Noninterior Continuation Methods
for Linear Complementarity Problems . . 851--868
Christian H. Bischof and
Xiaobai Sun On Tridiagonalizing and Diagonalizing
Symmetric Matrices with Repeated
Eigenvalues . . . . . . . . . . . . . . 869--885
Patrick R. Amestoy and
Timothy A. Davis and
Iain S. Duff An Approximate Minimum Degree Ordering
Algorithm . . . . . . . . . . . . . . . 886--905
Dario Bini and
Beatrice Meini On the Solution of a Nonlinear Matrix
Equation Arising in Queueing Problems 906--926
A. S. Lewis Group Invariance and Convex Matrix
Analysis . . . . . . . . . . . . . . . . 927--949
S. Chandrasekaran and
Ali H. Sayed Stabilizing the Generalized Schur
Algorithm . . . . . . . . . . . . . . . 950--983
Steven L. Lee Best Available Bounds For Departure From
Normality . . . . . . . . . . . . . . . 984--991
Jean-Pierre Crouzeix and
Siegfried Schaible Generalized Monotone Affine Maps . . . . 992--997
Takashi Ito Every Normal Toeplitz Matrix is Either
of Type I or of Type II . . . . . . . . 998--1006
Stefano Serra Preconditioning Strategies for Hermitian
Toeplitz Systems with Nondefinite
Generating Functions . . . . . . . . . . 1007--1019
Ji\vrí Rohn and
Georg Rex Interval $ {P}$-matrices . . . . . . . . 1020--1024
J. J. McDonald and
M. Neumann and
H. Schneider and
M. J. Tsatsomeros Inverses of Unipathic $M$-Matrices . . . 1025--1036
Douglas R. Farenick and
Mark Krupnik and
Naum Krupnik and
Woo Young Lee Normal Toeplitz Matrices . . . . . . . . 1037--1043
Karl Meerbergen and
Dirk Roose The Restarted Arnoldi Method Applied to
Iterative Linear System Solvers for the
Computation of Rightmost Eigenvalues . . 1--20
Zlatko Drma\vc and
Vjeran Hari Relative Residual Bounds for the
Eigenvalues of a Hermitian Semidefinite
Matrix . . . . . . . . . . . . . . . . . 21--29
Kim-Chuan Toh GMRES vs. Ideal GMRES . . . . . . . . . 30--36
Peter N. Brown and
Homer F. Walker GMRES On (Nearly) Singular Systems . . . 37--51
Nicholas J. Higham Stability of the Diagonal Pivoting
Method with Partial Pivoting . . . . . . 52--65
Wasin So and
Jianzhong Wang Estimating the Support of a Scaling
Vector . . . . . . . . . . . . . . . . . 66--73
Natália Bebiano and
Chi-Kwong Li and
João da Providência Determinant of the Sum of a Symmetric
and a Skew-Symmetric Matrix . . . . . . 74--82
S. M. Rump Bounds for the Componentwise Distance to
the Nearest Singular Matrix . . . . . . 83--103
Michael Stewart and
Paul Van Dooren Stability Issues in the Factorization of
Structured Matrices . . . . . . . . . . 104--118
M. Ali\'c and
B. Mond and
J. Pe\vcari\'c and
V. Volenec Bounds for the Differences of Matrix
Means . . . . . . . . . . . . . . . . . 119--123
Lars-Erik Andersson and
Tommy Elfving A Constrained Procrustes Problem . . . . 124--139
Timothy A. Davis and
Iain S. Duff An Unsymmetric-Pattern Multifrontal
Method for Sparse $ L U $ Factorization 140--158
Daniel J. Pierce and
John G. Lewis Sparse Multifrontal Rank Revealing $ Q R
$ Factorization . . . . . . . . . . . . 159--180
S. R. Mohan and
S. K. Neogy Vertical Block Hidden $Z$-Matrices and
the Generalized Linear Complementarity
Problem . . . . . . . . . . . . . . . . 181--190
Stephen Wright Stability of augmented system
factorizations in interior-point methods 191--222
Qi-Ming He and
Marcel F. Neuts On Episodic Queues . . . . . . . . . . . 223--248
Daniel Hershkowitz and
Wenchao Huang and
Hans Schneider and
Hans Weinberger Approximability by Weighted Norms of the
Structured and Volumetric Singular
Values of a Class of Nonnegative
Matrices . . . . . . . . . . . . . . . . 249--257
Rajendra Bhatia and
Fuad Kittaneh Some Inequalities for Norms of
Commutators . . . . . . . . . . . . . . 258--263
Alan George and
Kh. Ikramov Addendum: ``Is the polar decomposition
finitely computable?'' [SIAM J. Matrix
Anal. Appl. \bf 17 (1996), no. 2,
348--354,MR 96m:15023] . . . . . . . . . 264--264
A. N. Malyshev and
M. Sadkane On Parabolic and Elliptic Spectral
Dichotomy . . . . . . . . . . . . . . . 265--278
A. Scottedward Hodel and
Pradeep Misra Least-Squares Approximate Solution of
Overdetermined Sylvester Equations . . . 279--290
Emmanuel G. Collins, Jr. and
A. Scottedward Hodel Efficient Solution of Linearly Coupled
Lyapunov Equations . . . . . . . . . . . 291--304
Jianzhou Liu and
Li Zhu Some Improvement of Oppenheim's
Inequality for $M$-Matrices . . . . . . 305--311
S. H. Lui and
H. B. Keller and
T. W. C. Kwok Homotopy Method for the Large, Sparse,
Real Nonsymmetric Eigenvalue Problem . . 312--333
Wenchao Huang and
Chi-Kwong Li and
Hans Schneider Norms and Inequalities Related to Schur
Products of Rectangular Matrices . . . . 334--347
S. Yu and
G. A. Latham and
R. S. Anderssen Matrix Analysis of a Two-Stage-Splitting
Iteration for Maximum Penalized
Likelihood Estimation . . . . . . . . . 348--359
Leonid Gurvits and
Leiba Rodman Convergence of Polynomially Bounded
Semigroups of Matrices . . . . . . . . . 360--368
Patricia D. Hough and
Stephen A. Vavasis Complete Orthogonal Decomposition for
Weighted Least Squares . . . . . . . . . 369--392
Ji-guang Sun and
Zheng Sun Optimal Backward Perturbation Bounds for
Underdetermined Systems . . . . . . . . 393--402
Ilan Bar-On and
Bruno Codenotti and
Mauro Leoncini A Fast Parallel Cholesky Decomposition
Algorithm for Tridiagonal Symmetric
Matrices . . . . . . . . . . . . . . . . 403--418
V. Simoncini A Stabilized QMR Version of Block BiCG 419--434
Yousef Saad Analysis of Augmented Krylov Subspace
Methods . . . . . . . . . . . . . . . . 435--449
B. Kalantari and
L. Khachiyan and
A. Shokoufandeh On the Complexity of Matrix Balancing 450--463
Wai Ki Ching and
Raymond H. Chan and
Xun Yu Zhou Circulant Preconditioners for
Markov-Modulated Poisson Processes and
Their Applications to Manufacturing
Systems . . . . . . . . . . . . . . . . 464--481
Tu\ugrul Dayar and
William J. Stewart Quasi Lumpability, Lower-Bounding
Coupling Matrices, and Nearly Completely
Decomposable Markov Chains . . . . . . . 482--498
Man-Chung Yeung and
Tony F. Chan Probabilistic Analysis of Gaussian
Elimination without Pivoting . . . . . . 499--517
Khakim D. Ikramov Comments on: ``Normal Toeplitz
matrices'' [SIAM J. Matrix Anal.\ Appl.
\bf 17 (1996), no. 4, 1037--1043 and MR
97g:15025] by D. R. Farenick, M.
Krupnik, N. Krupnik, and W. Y. Lee . . . 518--518
Anonymous List of Referees . . . . . . . . . . . . 519--520
Wolfgang Mackens and
Heinrich Voss The Minimum Eigenvalue of a Symmetric
Positive-Definite Toeplitz Matrix and
Rational Hermitian Interpolation . . . . 521--534
Anne Greenbaum Estimating the Attainable Accuracy of
Recursively Computed Residual Methods 535--551
Shang-Hua Teng Fast Nested Dissection for Finite
Element Meshes . . . . . . . . . . . . . 552--565
David Day An Efficient Implementation of the
Nonsymmetric Lanczos Algorithm . . . . . 566--589
Wen-Wei Lin and
Chern-Shuh Wang On Computing Stable Lagrangian Subspaces
of Hamiltonian Matrices and Symplectic
Pencils . . . . . . . . . . . . . . . . 590--614
Ralph Byers and
Chunyang He and
Volker Mehrmann The Matrix Sign Function Method and the
Computation of Invariant Subspaces . . . 615--632
Imad M. Jaimoukha and
Ebrahim M. Kasenally Implicitly Restarted Krylov Subspace
Methods for Stable Partial Realizations 633--652
Alan Edelman and
Erik Elmroth and
Bo Kågström A Geometric Approach to Perturbation
Theory of Matrices and Matrix Pencils.
Part I: Versal Deformations . . . . . . 653--692
Götz Alefeld and
Vladik Kreinovich and
Günter Mayer On the Shape of the Symmetric,
Persymmetric, and Skew-Symmetric
Solution Set . . . . . . . . . . . . . . 693--705
Alan George and
Alex Pothen An Analysis of Spectral Envelope
Reduction via Quadratic Assignment
Problems . . . . . . . . . . . . . . . . 706--732
Howard C. Elman Perturbation of Eigenvalues of
Preconditioned Navier--Stokes Operators 733--751
Yuri Bolshakov and
Cornelis V. M. van der Mee and
André C. M. Ran and
Boris Reichstein and
Leiba Rodman Extension of Isometries in
Finite-Dimensional Indefinite Scalar
Product Spaces and Polar Decompositions 752--774
Xiao-Wen Chang and
Christopher C. Paige and
G. W. Stewart Perturbation Analyses for the $ Q R $
Factorization . . . . . . . . . . . . . 775--791
Julio Moro and
James V. Burke and
Michael L. Overton On the Lidskii--Vishik Lyusternik
Perturbation Theory for Eigenvalues of
Matrices with Arbitrary Jordan Structure 793--817
J. P. Le Cadre and
O. Trémois The Matrix Dynamic Programming Property
and Its Implications . . . . . . . . . . 818--826
Stephen J. Kirkland and
Michael Neumann and
Bryan L. Shader Distances in Weighted Trees and Group
Inverse of Laplacian Matrices . . . . . 827--841
Tin Yau Tam On the Behavior of a Sequence Defined by
a Periodic Recursive Relation . . . . . 842--860
Roy Mathias A Bound for the Matrix Square Root with
Application to Eigenvector Perturbation 861--867
Thorkell Gudmundsson and
Charles Kenney and
Alan J. Laub Small-Sample Statistical Estimates for
the Sensitivity of Eigenvalue Problems 868--886
Jürgen Gross A Note on a Partial Ordering in the Set
of Hermitian Matrices . . . . . . . . . 887--892
Andreas Frommer and
Hartmut Schwandt A Unified Representation and Theory of
Algebraic Additive Schwarz and
Multisplitting Methods . . . . . . . . . 893--912
Gianna M. Del Corso Estimating an Eigenvector by the Power
Method with a Random Start . . . . . . . 913--937
Roger Fletcher and
Tom Johnson On the Stability of Null-Space Methods
for KKT Systems . . . . . . . . . . . . 938--958
Roy Mathias Spectral Perturbation Bounds for
Positive Definite Matrices . . . . . . . 959--980
Radka Turcajová Numerical Condition of Discrete Wavelet
Transforms . . . . . . . . . . . . . . . 981--999
Vjeran Hari and
Zlatko Drma\vc On scaled almost-diagonal Hermitian
matrix pairs . . . . . . . . . . . . . . 1000--1012
K. V. Fernando On Computing an Eigenvector of a
Tridiagonal Matrix. Part I: Basic
Results . . . . . . . . . . . . . . . . 1013--1034
Laurent El Ghaoui and
Hervé Lebret Robust Solutions to Least-Squares
Problems with Uncertain Data . . . . . . 1035--1064
Sivan Toledo Locality of Reference in $ L U $
Decomposition with Partial Pivoting . . 1065--1081
Moody T. Chu and
Robert E. Funderlic and
Gene H. Golub On a Variational Formulation of the
Generalized Singular Value Decomposition 1082--1092
Xingzhi Zhan Inequalities for the Singular Values of
Hadamard Products . . . . . . . . . . . 1093--1095
Moody T. Chu and
Quanlin Guo On the Least Squares Approximation of
Symmetric-Definite Pencils Subject to
Generalized Spectral Constraints . . . . 1--20
D. L. Chu and
H. C. Chan and
D. W. C. Ho Regularization of Singular Systems by
Derivative and Proportional Output
Feedback . . . . . . . . . . . . . . . . 21--38
Ji-guang Sun Perturbation Theory for Algebraic
Riccati Equations . . . . . . . . . . . 39--65
B. Mond and
J. E. Pecaric Inequalities for the Hadamard Product of
Matrices . . . . . . . . . . . . . . . . 66--70
Ettore Fornasini and
Maria Elena Valcher Primitivity of Positive Matrix Pairs:
Algebraic Characterization, Graph
Theoretic Description, and 2D Systems
Interpretation . . . . . . . . . . . . . 71--88
O. H. Odeh and
D. D. Olesky and
P. van den Driessche Bruhat Decomposition and Numerical
Stability . . . . . . . . . . . . . . . 89--98
Chi-Kwong Li and
Roy Mathias Generalizations of Ky Fan's Dominance
Theorem . . . . . . . . . . . . . . . . 99--106
S. Chandrasekaran and
Ali H. Sayed A Fast Stable Solver for Nonsymmetric
Toeplitz and Quasi-Toeplitz Systems of
Linear Equations . . . . . . . . . . . . 107--139
Hsin-Chu Chen Generalized Reflexive Matrices: Special
Properties and Applications . . . . . . 140--153
Anders Barrlund Efficient Solution of Constrained Least
Squares Problems with Kronecker Product
Structure . . . . . . . . . . . . . . . 154--160
Luca Gemignani Computing a Factor of a Polynomial by
Means of Multishift $ L R $ Algorithms 161--181
D. J. Hartfiel Eigenvector Slicing of the Nonnegative
Matrices . . . . . . . . . . . . . . . . 182--190
Apostolos Hadjidimos and
Michael Neumann Euclidean Norm Minimization of the SOR
Operators . . . . . . . . . . . . . . . 191--204
Zhaojun Bai and
James Demmel Using the Matrix Sign Function to
Compute Invariant Subspaces . . . . . . 205--225
Stephen J. Kirkland and
Michael Neumann The $M$-Matrix Group Generalized Inverse
Problem for Weighted Trees . . . . . . . 226--234
S. Chandrasekaran and
G. H. Golub and
M. Gu and
A. H. Sayed Parameter Estimation in the Presence of
Bounded Data Uncertainties . . . . . . . 235--252
Hao Lu A Generalized Hilbert Matrix Problem and
Confluent Chebyshev--Vandermonde Systems 253--276
Dao-Sheng Zheng Note On ``Further Study and
Generalization of Kahan's Matrix
Extension Theorem'' . . . . . . . . . . 277--278
Ming Gu Stable and Efficient Algorithms for
Structured Systems of Linear Equations 279--306
Ilya Krupnik and
Peter Lancaster $H$-Selfadjoint and $H$-Unitary Matrix
Pencils . . . . . . . . . . . . . . . . 307--324
Cleve Ashcraft and
Joseph W. H. Liu Applications of the Dulmage--Mendelsohn
Decomposition and Network Flow to Graph
Bisection Improvement . . . . . . . . . 325--354
Michael J. Tsatsomeros Sign Controllability: Sign Patterns That
Require Complete Controllability . . . . 355--364
Jürgen Gross More on Concavity of a Matrix Function 365--368
J. M. Peña On the Relationship Between Graphs and
Totally Positive Matrices . . . . . . . 369--377
Bart De Schutter and
Bart De Moor The $ Q R $ Decomposition and the
Singular Value Decomposition in the
Symmetrized Max-Plus Algebra . . . . . . 378--406
Yiju Wang On the Block Independence in Reflexive
Inner Inverse and $M$-$P$ Inverse of
Block Matrix . . . . . . . . . . . . . . 407--415
Cen Jianmiao On the Sandwich Semigroups of Group
Boolean Matrices . . . . . . . . . . . . 416--428
Xiao-Wen Chang and
Christopher C. Paige Perturbation Analyses for the Cholesky
Downdating Problem . . . . . . . . . . . 429--443
Mark Arnold and
Biswa Nath Datta Single-Input Eigenvalue Assignment
Algorithms: a Close Look . . . . . . . . 444--467
Hongyuan Zha and
Zhenyue Zhang A Cubically Convergent Parallelizable
Method for the Hermitian Eigenvalue
Problem . . . . . . . . . . . . . . . . 468--486
Tsuyoshi Ando and
Mau-hsiang Shih Simultaneous Contractibility . . . . . . 487--498
Lieven Vandenberghe and
Stephen Boyd and
Shao-Po Wu Determinant Maximization with Linear
Matrix Inequality Constraints . . . . . 499--533
Daniel P. Heyman and
Dianne P. O'Leary Overcoming Instability in Computing the
Fundamental Matrix for a Markov Chain 534--540
Roy Mathias Quadratic Residual Bounds for the
Hermitian Eigenvalue Problem . . . . . . 541--550
Hongguo Xu The Relation Between the $ Q R $ and $ L
R $ Algorithms . . . . . . . . . . . . . 551--555
E. Seneta Complementation in Stochastic Matrices
and the GTH Algorithm . . . . . . . . . 556--563
D. Viswanath and
L. N. Trefethen Condition Numbers of Random Triangular
Matrices . . . . . . . . . . . . . . . . 564--581
Nir Cohen and
Jerome Dancis Inertias of Block Band Matrix
Completions . . . . . . . . . . . . . . 583--612
Geir Nævdal and
Hugo J. Woerdeman Cone Inclusion Numbers . . . . . . . . . 613--639
C. S. Kenney and
A. J. Laub A Schur--Fréchet Algorithm for Computing
the Logarithm and Exponential of a
Matrix . . . . . . . . . . . . . . . . . 640--663
Volker Mehrmann and
Hongguo Xu Choosing Poles So That the Single-Input
Pole Placement Problem Is Well
Conditioned . . . . . . . . . . . . . . 664--681
Edward Rothberg and
Stanley C. Eisenstat Node Selection Strategies for Bottom-Up
Sparse Matrix Ordering . . . . . . . . . 682--695
Jiu Ding Perturbation Results for Projecting a
Point onto a Linear Manifold . . . . . . 696--700
Stephen Guattery and
Gary L. Miller On the Quality of Spectral Separators 701--719
Åke Björck and
Tommy Elfving and
Zdenek Strakos Stability of Conjugate Gradient and
Lanczos Methods for Linear Least Squares
Problems . . . . . . . . . . . . . . . . 720--736
Tin-Yau Tam Partial Superdiagonal Elements and
Singular Values of a Complex
Skew-Symmetric Matrix . . . . . . . . . 737--754
Vladimir Druskin and
Leonid Knizhnerman Extended Krylov Subspaces: Approximation
of the Matrix Square Root and Related
Functions . . . . . . . . . . . . . . . 755--771
Wenyu Sun and
Yimin Wei Inverse Order Rule for Weighted
Generalized Inverse . . . . . . . . . . 772--775
Inderjit S. Dhillon Reliable Computation of the Condition
Number of a Tridiagonal Matrix in $ O(n)
$ Time . . . . . . . . . . . . . . . . . 776--796
Xu Zhong and
You Zhaoyong A Fast Algorithm for Inversion of
Confluent Vandermonde-Like Matrices
Involving Polynomials that Satisfy a
Three-Term Recurrence Relation . . . . . 797--806
Jesse L. Barlow and
Hongyuan Zha Growth in Gaussian Elimination,
Orthogonal Matrices, and the $2$-Norm 807--815
Cleve Ashcraft and
Joseph W. H. Liu Robust Ordering of Sparse Matrices using
Multisection . . . . . . . . . . . . . . 816--832
Ya Yan Lu A Padé Approximation Method for Square
Roots of Symmetric Positive Definite
Matrices . . . . . . . . . . . . . . . . 833--845
Michael Stewart and
G. W. Stewart On Hyperbolic Triangularization:
Stability and Pivoting . . . . . . . . . 847--860
Charles R. Johnson and
Pablo Tarazaga Approximate Semidefinite Matrices in a
Linear Variety . . . . . . . . . . . . . 861--871
M. I. García-Planas Kronecker Stratification of the Space of
Quadruples of Matrices . . . . . . . . . 872--885
Licio H. Bezerra and
Fermin S. V. Bazán Eigenvalue Locations of Generalized
Companion Predictor Matrices . . . . . . 886--897
G. S. R. Murthy and
T. Parthasarathy and
B. Sriparna Some Recent Results on The Linear
Complementarity Problem . . . . . . . . 898--905
C. S. Kenney and
A. J. Laub and
M. S. Reese Statistical Condition Estimation for
Linear Least Squares . . . . . . . . . . 906--923
Josep Ferrer and
Ferran Puerta Global Block-Similarity and Pole
Assignment of Class $C^p$ . . . . . . . 924--932
Wei-Yong Yan Stability and Convergence of Principal
Component Learning Algorithms . . . . . 933--955
Ren-Cang Li Relative Perturbation Theory: I.
Eigenvalue and Singular Value Variations 956--982
Rik Pintelon and
Patrick Guillaume and
Gerd Vandersteen and
Yves Rolain Analyses, Development, and Applications
of TLS Algorithms in Frequency Domain
System Identification . . . . . . . . . 983--1004
Mohsen Maesumi On Construction of a Family of Smooth
Nonseparable Prewavelets via Infinite
Products of Triangularizable Matrices 1005--1026
Moody T. Chu and
Quanlin Guo A Numerical Method for the Inverse
Stochastic Spectrum Problem . . . . . . 1027--1039
Bo-Ying Wang On the Singularity of LCM Matrices . . . 1040--1044
D. C. Sorensen and
C. Yang A Truncated RQ Iteration for Large Scale
Eigenvalue Calculations . . . . . . . . 1045--1073
David S. Watkins Bulge Exchanges in Algorithms of $ Q R $
Type . . . . . . . . . . . . . . . . . . 1074--1096
Sheung Hun Cheng and
Nicholas J. Higham A Modified Cholesky Algorithm Based on a
Symmetric Indefinite Factorization . . . 1097--1110
Robert E. Hartwig and
Peter Semrl Power Additivity and Orthogonality . . . 1--13
J. B. Rosen and
Haesun Park and
John Glick Structured Total Least Norm for
Nonlinear Problems . . . . . . . . . . . 14--30
Stefano Serra Asymptotic Results on the Spectra of
Block Toeplitz Preconditioned Matrices 31--44
Ji-guang Sun Bounds for the Structured Backward
Errors of Vandermonde Systems . . . . . 45--59
William M. Spears A Compression Algorithm for Probability
Transition Matrices . . . . . . . . . . 60--77
Alan L. Andrew and
Roger C. E. Tan Computation of Derivatives of Repeated
Eigenvalues and the Corresponding
Eigenvectors of Symmetric Matrix Pencils 78--100
C. He and
G. A. Watson An Algorithm for Computing the Distance
to Instability . . . . . . . . . . . . . 101--116
Wayne W. Barrett and
Charles R. Johnson and
Raphael Loewy Critical Graphs for the Positive
Definite Completion Problem . . . . . . 117--130
R. B. Lehoucq and
Karl Meerbergen Using Generalized Cayley Transformations
within an Inexact Rational Krylov
Sequence Method . . . . . . . . . . . . 131--148
Stanley C. Eisenstat and
Ilse C. F. Ipsen Three Absolute Perturbation Bounds for
Matrix Eigenvalues Imply Relative Bounds 149--158
Plamen Yalamov and
Velisar Pavlov On the Stability of a Partitioning
Algorithm for Tridiagonal Systems . . . 159--181
Martin Bohner and
Ondrej Doslý Positivity of Block Tridiagonal Matrices 182--195
Kazuo Murota On the Degree of Mixed Polynomial
Matrices . . . . . . . . . . . . . . . . 196--227
Jonq Juang and
Wen-Wei Lin Nonsymmetric Algebraic Riccati Equations
and Hamiltonian-like Matrices . . . . . 228--243
Ming Gu New Fast Algorithms for Structured
Linear Least Squares Problems . . . . . 244--269
Jungong Xue and
Weiguo Gao Blockwise Perturbation Theory for Markov
Chains . . . . . . . . . . . . . . . . . 270--278
Chun-Hua Guo Newton's Method for Discrete Algebraic
Riccati Equations when the Closed-Loop
Matrix Has Eigenvalues on the Unit
Circle . . . . . . . . . . . . . . . . . 279--294
H. W. Braden The Equations $ A^T X \pm X^T A = B $ 295--302
Alan Edelman and
Tomás A. Arias and
Steven T. Smith The Geometry of Algorithms with
Orthogonality Constraints . . . . . . . 303--353
S. Chandrasekaran and
M. Gu and
A. H. Sayed A Stable and Efficient Algorithm for the
Indefinite Linear Least-Squares Problem 354--362
Ming Gu Backward Perturbation Bounds for Linear
Least Squares Problems . . . . . . . . . 363--372
K. V. Fernando Accurately Counting Singular Values of
Bidiagonal Matrices and Eigenvalues of
Skew-Symmetric Tridiagonal Matrices . . 373--399
Kim-Chuan Toh and
Lloyd N. Trefethen The Chebyshev Polynomials of a Matrix 400--419
Branko Najman The Asymptotic Behavior of the
Eigenvalues of a Singularly Perturbed
Linear Pencil . . . . . . . . . . . . . 420--427
Moody T. Chu and
R. E. Funderlic and
Gene H. Golub Rank Modifications of Semidefinite
Matrices Associated with a Secant Update
Formula . . . . . . . . . . . . . . . . 428--436
Georg Rex and
Jiri Rohn Sufficient Conditions for Regularity and
Singularity of Interval Matrices . . . . 437--445
Stefano Serra Capizzano Toeplitz Preconditioners Constructed
from Linear Approximation Processes . . 446--465
Xingzhi Zhan Inequalities for Unitarily Invariant
Norms . . . . . . . . . . . . . . . . . 466--470
Ren-Cang Li Relative Perturbation Theory: II.
Eigenspace and Singular Subspace
Variations . . . . . . . . . . . . . . . 471--492
Desmond J. Higham and
Nicholas J. Higham Structured Backward Error and Condition
of Generalized Eigenvalue Problems . . . 493--512
Cleve Ashcraft and
Roger G. Grimes and
John G. Lewis Accurate Symmetric Indefinite Linear
Equation Solvers . . . . . . . . . . . . 513--561
S. Elhay and
G. M. L. Gladwell and
G. H. Golub and
Y. M. Ram On Some Eigenvector-Eigenvalue Relations 563--574
Philippe Guillaume Nonlinear Eigenproblems . . . . . . . . 575--595
Pachara Chaisuriya and
Sing-Cheong Ong Absolute Schur Algebras and Unbounded
Matrices . . . . . . . . . . . . . . . . 596--605
Timothy A. Davis and
William W. Hager Modifying a Sparse Cholesky
Factorization . . . . . . . . . . . . . 606--627
Tuomo Rossi and
Jari Toivanen A Nonstandard Cyclic Reduction Method,
Its Variants and Stability . . . . . . . 628--645
Inmaculada Higueras and
Berta Garcia-Celayeta Logarithmic Norms for Matrix Pencils . . 646--666
Alan Edelman and
Erik Elmroth and
Bo Kågström A Geometric Approach to Perturbation
Theory of Matrices and Matrix Pencils.
Part II: a Stratification-Enhanced
Staircase Algorithm . . . . . . . . . . 667--699
Dario Andrea Bini and
Beatrice Meini Effective Methods for Solving Banded
Toeplitz Systems . . . . . . . . . . . . 700--719
James W. Demmel and
Stanley C. Eisenstat and
John R. Gilbert and
Xiaoye S. Li and
Joseph W. H. Liu A Supernodal Approach to Sparse Partial
Pivoting . . . . . . . . . . . . . . . . 720--755
Christian Jansson and
Jiri Rohn An Algorithm for Checking Regularity of
Interval Matrices . . . . . . . . . . . 756--776
Misha E. Kilmer Cauchy-like Preconditioners for
Two-Dimensional Ill-Posed Problems . . . 777--799
Luca Dieci and
Timo Eirola On Smooth Decompositions of Matrices . . 800--819
Reinhard Nabben Decay Rates of the Inverse of
Nonsymmetric Tridiagonal and Band
Matrices . . . . . . . . . . . . . . . . 820--837
S. Chandrasekaran and
G. H. Golub and
M. Gu and
A. H. Sayed An Efficient Algorithm for a Bounded
Errors-in-Variables Model . . . . . . . 839--859
Stephen J. Kirkland and
Michael Neumann Cutpoint Decoupling and First Passage
Times for Random Walks on Graphs . . . . 860--870
Qi-Ming He Partial Orders and the Matrix $R$ in
Matrix Analytic Methods . . . . . . . . 871--885
Esmond G. Ng and
Daniel J. Pierce Introduction to the Special Section on
Sparse and Structured Matrices and Their
Applications . . . . . . . . . . . . . . 887--887
Iain S. Duff and
Jacko Koster The Design and Use of Algorithms for
Permuting Large Entries to the Diagonal
of Sparse Matrices . . . . . . . . . . . 889--901
Esmond G. Ng and
Padma Raghavan Performance of Greedy Ordering
Heuristics for Sparse Cholesky
Factorization . . . . . . . . . . . . . 902--914
James W. Demmel and
John R. Gilbert and
Xiaoye S. Li An Asynchronous Parallel Supernodal
Algorithm for Sparse Gaussian
Elimination . . . . . . . . . . . . . . 915--952
Alan George and
Joseph Liu An Object-Oriented Approach to the
Design of a User Interface for a Sparse
Matrix Package . . . . . . . . . . . . . 953--969
Wei-Pai Tang Toward an Effective Sparse Approximate
Inverse Preconditioner . . . . . . . . . 970--986
Arno C. N. van Duin Scalable Parallel Preconditioning with
the Sparse Approximate Inverse of
Triangular Matrices . . . . . . . . . . 987--1006
E. F. F. Botta and
F. W. Wubs Matrix Renumbering ILU: An Effective
Algebraic Multilevel ILU Preconditioner
for Sparse Matrices . . . . . . . . . . 1007--1026
Curtis R. Vogel Sparse Matrix Computations Arising in
Distributed Parameter Identification . . 1027--1037
Chen Greif and
James Varah Block Stationary Methods for
Nonsymmetric Cyclically Reduced Systems
Arising from Three-Dimensional Elliptic
Equations . . . . . . . . . . . . . . . 1038--1059
Zhaojun Bai and
David Day and
Qiang Ye ABLE: An Adaptive Block Lanczos Method
for Non-Hermitian Eigenvalue Problems 1060--1082
G. A. Geist and
G. W. Howell and
D. S. Watkins The $ B R $ Eigenvalue Algorithm . . . . 1083--1098
Rong-Qing Jia and
Sherman D. Riemenschneider and
Ding-Xuan Zhou Smoothness of Multiple Refinable
Functions and Multiple Wavelets . . . . 1--28
Chen Greif Reduced Systems for Three-Dimensional
Elliptic Equations with Variable
Coefficients . . . . . . . . . . . . . . 29--44
Hou-Duo Qi and
Li-Zhi Liao A Smoothing Newton Method for Extended
Vertical Linear Complementarity Problems 45--66
Zhong-Zhi Bai On the Convergence of the Multisplitting
Methods for the Linear Complementarity
Problem . . . . . . . . . . . . . . . . 67--78
Lixing Han and
Michael Neumann and
Michael Tsatsomeros Spectral Radii of Fixed Frobenius Norm
Perturbations of Nonnegative Matrices 79--92
Adam L. Cohen and
Leiba Rodman and
David P. Stanford Pointwise and Uniformly Convergent Sets
of Matrices . . . . . . . . . . . . . . 93--105
Alexei A. Mailybaev and
Alexander P. Seyranian On Singularities of a Boundary of the
Stability Domain . . . . . . . . . . . . 106--128
Onn Chan and
T. K. Lam Immanant Inequalities for Laplacians of
Trees . . . . . . . . . . . . . . . . . 129--144
Kim-Chuan Toh and
Lloyd N. Trefethen The Kreiss Matrix Theorem on a General
Complex Domain . . . . . . . . . . . . . 145--165
Steven J. Benbow Solving Generalized Least-Squares
Problems with LSQR . . . . . . . . . . . 166--177
Hyungju Park A Realization Algorithm for $ S L_2
(R[x_1, \ldots {}, x_m]) $ over the
Euclidean Domain . . . . . . . . . . . . 178--184
Gene H. Golub and
Per Christian Hansen and
Dianne P. O'Leary Tikhonov Regularization and Total Least
Squares . . . . . . . . . . . . . . . . 185--194
Pedro Freitas and
Peter Lancaster On the Optimal Value of the Spectral
Abscissa for a System of Linear
Oscillators . . . . . . . . . . . . . . 195--208
Kurt Otto and
Elisabeth Larsson Iterative Solution of the Helmholtz
Equation by a Second-Order Method . . . 209--229
J. Maroulas and
M. Adam Compressions and Dilations of Numerical
Ranges . . . . . . . . . . . . . . . . . 230--244
Cristian Oarua and
Andras Varga Minimal Degree Coprime Factorization of
Rational Matrices . . . . . . . . . . . 245--278
Yousef Saad and
Jun Zhang BILUTM: a Domain-Based Multilevel Block
ILUT Preconditioner for General Sparse
Matrices . . . . . . . . . . . . . . . . 279--299
Adi Ben-Israel The Change-of-Variables Formula Using
Matrix Volume . . . . . . . . . . . . . 300--312
Anthony J. Cox and
Nicholas J. Higham Row-Wise Backward Stable Elimination
Methods for the Equality Constrained
Least Squares Problem . . . . . . . . . 313--326
M. Konstantinov and
P. Petkov Note on Perturbation Theory for
Algebraic Riccati Equations . . . . . . 327--327
Bart De Schutter and
Bart De Moor On the Sequence of Consecutive Powers of
a Matrix in a Boolean Algebra . . . . . 328--354
Tristan Londré and
Noah H. Rhee A Note on Relative Perturbation Bounds 357--361
A. Melman Bounds on the Extreme Eigenvalues of
Real Symmetric Toeplitz Matrices . . . . 362--378
A. S. Lewis Lidskii's Theorem via Nonsmooth Analysis 379--381
L. Kohaupt Second Logarithmic Derivative of a
Complex Matrix in the Chebyshev Norm . . 382--389
Jürgen Gross and
Götz Trenkler Nonsingularity of the Difference of Two
Oblique Projectors . . . . . . . . . . . 390--395
Alexei A. Mailybaev Transformation of Families of Matrices
to Normal Forms and its Application to
Stability Theory . . . . . . . . . . . . 396--417
Rong-Qing Jia and
Ding-Xuan Zhou Convergence of Subdivision Schemes
Associated with Nonnegative Masks . . . 418--430
S. Serra Capizzano and
E. Tyrtyshnikov Any Circulant-Like Preconditioner for
Multilevel Matrices Is Not Superlinear 431--439
Ren-Cang Li A Bound on the Solution to a Structured
Sylvester Equation with an Application
to Relative Perturbation Theory . . . . 440--445
Craig S. MacInnes The Solution to a Structured Matrix
Approximation Problem Using Grassman
Coordinates . . . . . . . . . . . . . . 446--453
Christian Mehl Condensed Forms for
Skew-Hamiltonian/Hamiltonian Pencils . . 454--476
Zhanye Tong and
Ahmed Sameh On Optimal Banded Preconditioners for
the Five-Point Laplacian . . . . . . . . 477--480
I. Gohberg and
M. A. Kaashoek and
J. Kos Classification of Linear Periodic
Difference Equations under Periodic or
Kinematic Similarity . . . . . . . . . . 481--507
A. Hadjidimos and
E. N. Houstis and
J. R. Rice and
E. Vavalis Analysis of Iterative Line Spline
Collocation Methods for Elliptic Partial
Differential Equations . . . . . . . . . 508--521
Hongyuan Zha and
Zhenyue Zhang Matrices with Low-Rank-Plus-Shift
Structure: Partial SVD and Latent
Semantic Indexing . . . . . . . . . . . 522--536
D. J. Hartfiel Distribution of Entries in a
Substochastic Matrix Having Eigenvalues
Near $1$ . . . . . . . . . . . . . . . . 537--546
A. Böttcher and
S. Grudsky and
A. Kozak and
B. Silbermann Norms of Large Toeplitz Band Matrices 547--561
James Demmel Accurate Singular Value Decompositions
of Structured Matrices . . . . . . . . . 562--580
Tin-Yau Tam Interlacing Inequalities and Cartan
Subspaces of Classical Real Simple Lie
Algebras . . . . . . . . . . . . . . . . 581--592
Mark A. Mendlovitz More Results on Eigenvector Saddlepoints
and Eigenpolynomials . . . . . . . . . . 593--612
Misha Kilmer and
G. W. Stewart Iterative Regularization and MINRES . . 613--628
James Allen Fill and
Donniell E. Fishkind The Moore--Penrose Generalized Inverse
for Sums of Matrices . . . . . . . . . . 629--635
G. S. R. Murthy and
S. K. Neogy and
F. Thuijsman A Note on $ P_1 $- and Lipschitzian
Matrices . . . . . . . . . . . . . . . . 636--641
Zhang Xian and
Yang Zhongpeng and
Cao Chongguang Real Solutions of the Equation
\boldmath$ {\Phi }^t({A}) = \frac
{1}{n}J_n $ . . . . . . . . . . . . . . 642--645
Carmine Di Fiore Matrix Algebras and Displacement
Decompositions . . . . . . . . . . . . . 646--667
Chi-Kwong Li and
Yiu-Tung Poon Convexity of the Joint Numerical Range 668--678
Fermín S. V. Bazán Conditioning of Rectangular Vandermonde
Matrices with Nodes in the Unit Disk . . 679--693
Chun-Hua Guo and
Alan J. Laub On a Newton-Like Method for Solving
Algebraic Riccati Equations . . . . . . 694--698
Anders Barrlund The $p$-Relative Distance is a Metric 699--702
Stephen Guattery and
Gary L. Miller Graph Embeddings and Laplacian
Eigenvalues . . . . . . . . . . . . . . 703--723
J. Ferrer and
M. I. García and
F. Puerta Regularity of the Brunovsky--Kronecker
Stratification . . . . . . . . . . . . . 724--742
D. J. Clements A State-Space Approach to Indefinite
Spectral Factorization . . . . . . . . . 743--767
Teri Barth and
Thomas Manteuffel Multiple Recursion Conjugate Gradient
Algorithms Part I: Sufficient Conditions 768--796
Christophe Couvreur and
Yoram Bresler On the Optimality of the Backward Greedy
Algorithm for the Subset Selection
Problem . . . . . . . . . . . . . . . . 797--808
B. Bohnhorst and
A. Bunse-Gerstner and
H. Fassbender On the Perturbation Theory for Unitary
Eigenvalue Problems . . . . . . . . . . 809--824
M. Arioli The Use of $ Q R $ Factorization in
Sparse Quadratic Programming and
Backward Error Issues . . . . . . . . . 825--839
Immanuel M. Bomze Linear-Time Copositivity Detection for
Tridiagonal Matrices and Extension to
Block-Tridiagonality . . . . . . . . . . 840--848
Per Christian Hansen and
Plamen Y. Yalamov Stabilization by Perturbation of a $ 4
n^2 $ Toeplitz Solver . . . . . . . . . 849--866
M. Miranda and
P. Tilli Asymptotic Spectra of Hermitian Block
Toeplitz Matrices and Preconditioning
Results . . . . . . . . . . . . . . . . 867--881
Jörg Liesen Computable Convergence Bounds for GMRES 882--903
Zhongpeng Yang and
Jianzhou Liu Some Results on Oppenheim's Inequalities
for $M$-Matrices . . . . . . . . . . . . 904--912
Luca Dieci and
Alessandra Papini Conditioning and Padé Approximation of
the Logarithm of a Matrix . . . . . . . 913--930
Musheng Wei and
Alvaro R. De Pierro Upper Perturbation Bounds of Weighted
Projections, Weighted and Constrained
Least Squares Problems . . . . . . . . . 931--951
Christoph Helmberg Fixing Variables in Semidefinite
Relaxations . . . . . . . . . . . . . . 952--969
Alan George and
Kh. Ikramov On the Condition of Symmetric
Quasi-Definite Matrices . . . . . . . . 970--977
Shawn Cokus and
Victor Klee Decomposition Theorems for Conditional
Sign-Solvability and Sign-Solvability of
General Systems . . . . . . . . . . . . 978--988
Ming Gu New Methods for Estimating the Distance
to Uncontrollability . . . . . . . . . . 989--1003
Alan Edelman and
Yanyuan Ma Staircase Failures Explained by
Orthogonal Versal Forms . . . . . . . . 1004--1025
Zlatko Drmac New Accurate Algorithms for Singular
Value Decomposition of Matrix Triplets 1026--1050
Martin H. Gutknecht and
Klaus J. Ressel Look-Ahead Procedures for Lanczos-Type
Product Methods Based on Three-Term
Lanczos Recurrences . . . . . . . . . . 1051--1078
Oliver G. Ernst Residual-Minimizing Krylov Subspace
Methods for Stabilized Discretizations
of Convection-Diffusion Equations . . . 1079--1101
José A. De Doná and
Graham C. Goodwin and
Richard H. Middleton and
Iain Raeburn Convergence of Eigenvalues in
State-Discretization of Linear
Stochastic Systems . . . . . . . . . . . 1102--1111
Ronald B. Morgan Implicitly Restarted GMRES and Arnoldi
Methods for Nonsymmetric Systems of
Equations . . . . . . . . . . . . . . . 1112--1135
Lubomír Bakule and
José Rodellar and
Josep M. Rossell Structure of Expansion-Contraction
Matrices in the Inclusion Principle for
Dynamic Systems . . . . . . . . . . . . 1136--1155
Arnold Neumaier On Shary's Algebraic Approach for Linear
Interval Equations . . . . . . . . . . . 1156--1162
Bor Plestenjak A Continuation Method for a Right
Definite Two-Parameter Eigenvalue
Problem . . . . . . . . . . . . . . . . 1163--1184
Nicholas J. Higham and
Françoise Tisseur A Block Algorithm for Matrix $1$-Norm
Estimation, with an Application to
$1$-Norm Pseudospectra . . . . . . . . . 1185--1201
S. Chandrasekaran An Efficient and Stable Algorithm for
the Symmetric-Definite Generalized
Eigenvalue Problem . . . . . . . . . . . 1202--1228
G. S. R. Murthy and
T. Parthasarathy and
B. Sriparna On the Solution Sets of Linear
Complementarity Problems . . . . . . . . 1229--1235
Wei-Pai Tang and
Wing Lok Wan Sparse Approximate Inverse Smoother for
Multigrid . . . . . . . . . . . . . . . 1236--1252
Lieven De Lathauwer and
Bart De Moor and
Joos Vandewalle A Multilinear Singular Value
Decomposition . . . . . . . . . . . . . 1253--1278
Jocelyne Erhel and
Frédéric Guyomarc'h An Augmented Conjugate Gradient Method
for Solving Consecutive Symmetric
Positive Definite Linear Systems . . . . 1279--1299
Carsten Keller and
Nicholas I. M. Gould and
Andrew J. Wathen Constraint Preconditioning for
Indefinite Linear Systems . . . . . . . 1300--1317
Alan George and
Kh. Ikramov and
A. B. Kucherov Some Properties of Symmetric
Quasi-Definite Matrices . . . . . . . . 1318--1323
Lieven De Lathauwer and
Bart De Moor and
Joos Vandewalle On the Best Rank-1 and Rank-($ R_1 $, $
R_2 $, \ldots, $ R_N$) Approximation of
Higher-Order Tensors . . . . . . . . . . 1324--1342
Marc Artzrouni and
Olivier Gavart Nonlinear Matrix Iterative Processes and
Generalized Coefficients of Ergodicity 1343--1353
Stefano Serra Capizzano Locally $X$ Matrices, Spectral
Distributions, Preconditioning, and
Applications . . . . . . . . . . . . . . 1354--1388
Liu Hongwei and
Liu Sanyang A Counterexample of the Convexity of
Sums of Singular Values . . . . . . . . 1389--1391
Zhi-Hao Cao A Note on $P$-Regular Splitting of
Hermitian Matrix . . . . . . . . . . . . 1392--1393
Gene Golub and
Knut Sòlna and
Paul Van Dooren Computing the SVD of a General Matrix
Product/Quotient . . . . . . . . . . . . 1--19
Zhi-Hao Cao Convergence of Nested Iterative Methods
for Symmetric $P$-Regular Splittings . . 20--32
A. A. Dubrulle Householder Transformations Revisited 33--40
Kurt Anstreicher and
Henry Wolkowicz On Lagrangian Relaxation of Quadratic
Matrix Constraints . . . . . . . . . . . 41--55
Michael K. Tippett and
Stephen E. Cohn and
Ricardo Todling and
Dan Marchesin Conditioning of the Stable,
Discrete-Time Lyapunov Operator . . . . 56--65
J.-P. Crouzeix and
A. Hassouni and
A. Lahlou and
S. Schaible Positive Subdefinite Matrices,
Generalized Monotonicity, and Linear
Complementarity Problems . . . . . . . . 66--85
Georg Heinig and
Karla Rost Hartley Transform Representations of
Symmetric Toeplitz Matrix Inverses with
Application to Fast Matrix-Vector
Multiplication . . . . . . . . . . . . . 86--105
Miroslav Fiedler Special Ultrametric Matrices and Graphs 106--113
Bernhard Beckermann and
George Labahn Fraction-Free Computation of Matrix
Rational Interpolants and Matrix GCDs 114--144
Daniel S. Bernstein and
Charles F. Van Loan Rational Matrix Functions and Rank-$1$
Updates . . . . . . . . . . . . . . . . 145--154
Julie Kamm and
James G. Nagy Optimal Kronecker Product Approximation
of Block Toeplitz Matrices . . . . . . . 155--172
Zlatko Drmac On Principal Angles between Subspaces of
Euclidean Space . . . . . . . . . . . . 173--194
Leonid Knizhnerman On GMRES-Equivalent Bounded Operators 195--212
Martin H. Gutknecht and
Zdenvek Strakos Accuracy of Two Three-term and Three
Two-term Recurrences for Krylov Space
Solvers . . . . . . . . . . . . . . . . 213--229
Jesse L. Barlow Stable Computation with the Fundamental
Matrix of a Markov Chain . . . . . . . . 230--241
Markus Bröker and
Xinlong Zhou Characterization of Continuous,
Four-Coefficient Scaling Functions via
Matrix Spectral Radius . . . . . . . . . 242--257
Albert Compta and
Josep Ferrer A Geometric Approach to the Carlson
Problem . . . . . . . . . . . . . . . . 258--275
Mårten Gulliksson and
Per-Åke Wedin The Use and Properties of Tikhonov
Filter Matrices . . . . . . . . . . . . 276--281
Kai Shen and
Tao Yang and
Xiangmin Jiao $ S^+ $: Efficient $2$D Sparse $ L U$
Factorization on Parallel Machines . . . 282--305
A. B. J. Kuijlaars Which Eigenvalues Are Found by the
Lanczos Method? . . . . . . . . . . . . 306--321
Ji-guang Sun Condition Number and Backward Error for
the Generalized Singular Value
Decomposition . . . . . . . . . . . . . 323--341
Peter Buchholz Multilevel Solutions for Structured
Markov Chains . . . . . . . . . . . . . 342--357
Plamen Y. Yalamov On the Almost Strong Stability of the
Circular Deconvolution Algorithm . . . . 358--363
David S. Watkins Performance of the $ Q Z $ Algorithm in
the Presence of Infinite Eigenvalues . . 364--375
Chun-Hua Guo and
Alan J. Laub On the Iterative Solution of a Class of
Nonsymmetric Algebraic Riccati Equations 376--391
Marina Arav and
Daniel Hershkowitz and
Volker Mehrmann Hans Schneider The Recursive Inverse Eigenvalue Problem 392--412
Åke Björck and
P. Heggernes and
P. Matstoms Methods for Large Scale Total Least
Squares Problems . . . . . . . . . . . . 413--429
V. Simoncini On the Convergence of Restarted Krylov
Subspace Methods . . . . . . . . . . . . 430--452
Maria Elena Valcher and
Lorenzo Farina An Algebraic Approach to the
Construction of Polyhedral Invariant
Cones . . . . . . . . . . . . . . . . . 453--471
Inmaculada Higueras and
Berta Garcia-Celayeta How Close Can the Logarithmic Norm of a
Matrix Pencil Come to the Spectral
Abscissa? . . . . . . . . . . . . . . . 472--478
Michael Stewart and
Paul Van Dooren Updating a Generalized $ U R V $
Decomposition . . . . . . . . . . . . . 479--500
Tim N. T. Goodman and
Charles A. Micchelli and
Giuseppe Rodriguez and
Sebastiano Seatzu On the Cholesky Factorization of the
Gram Matrix of Multivariate Functions 501--526
A. L. N. Murthy and
G. S. R. Murthy Principal Pivoting Method for Solving
Column Sufficient Complementarity
Problems . . . . . . . . . . . . . . . . 527--532
Nicola Mastronardi and
Philippe Lemmerling and
Sabine Van Huffel Fast Structured Total Least Squares
Algorithm for Solving the Basic
Deconvolution Problem . . . . . . . . . 533--553
R. E. White Multisplitting Methods: Optimal Schemes
for the Unknowns in a Given Overlap . . 554--568
Jaspal Singh Aujla Some Norm Inequalities for Completely
Monotone Functions . . . . . . . . . . . 569--573
Reinhard Nabben Improved Upper Bounds for the Real Part
of Nonmaximal Eigenvalues of Nonnegative
Matrices . . . . . . . . . . . . . . . . 574--579
Delin Chu and
Lieven De Lathauwer and
Bart De Moor On the Computation of the Restricted
Singular Value Decomposition via the
Cosine-Sine Decomposition . . . . . . . 580--601
Kesheng Wu and
Horst Simon Thick-Restart Lanczos Method for Large
Symmetric Eigenvalue Problems . . . . . 602--616
S. Pati Moore--Penrose Inverse of Matrices on
Idempotent Semirings . . . . . . . . . . 617--626
Shaun M. Fallat and
Michael I. Gekhtman and
Charles R. Johnson Spectral Structures of Irreducible
Totally Nonnegative Matrices . . . . . . 627--645
Raymond H. Chan and
Daniel Potts and
Gabriele Steidl Preconditioners for Nondefinite
Hermitian Toeplitz Systems . . . . . . . 647--665
Enrique Castillo and
Angel Cobo and
Francisco Jubete and
Rosa Eva Pruneda and
Carmen Castillo An Orthogonally Based Pivoting
Transformation of Matrices and Some
Applications . . . . . . . . . . . . . . 666--681
Peter Benner and
Heike Fassbender An Implicitly Restarted Symplectic
Lanczos Method for the Symplectic
Eigenvalue Problem . . . . . . . . . . . 682--713
Erricos J. Kontoghiorghes Parallel Strategies for Rank-$k$
Updating of the $ Q R$ Decomposition . . 714--725
Gerard L. G. Sleijpen and
Henk A. van der Vorst and
Jan Modersitzki Differences in the Effects of Rounding
Errors in Krylov Solvers for Symmetric
Indefinite Linear Systems . . . . . . . 726--751
Alan George and
Wei-Pai Tang and
Ya Dan Wu Multilevel One-Way Dissection
Factorization . . . . . . . . . . . . . 752--771
Jann-Long Chern and
Luca Dieci Smoothness and Periodicity of Some
Matrix Decompositions . . . . . . . . . 772--792
Alexander Padiy and
Owe Axelsson and
Ben Polman Generalized Augmented Matrix
Preconditioning Approach and its
Application to Iterative Solution of
Ill-Conditioned Algebraic Systems . . . 793--818
Xingzhi Zhan Singular Values of Differences of
Positive Semidefinite Matrices . . . . . 819--823
Timo Eirola A Refined Polar Decomposition: $ A = U P
D $ . . . . . . . . . . . . . . . . . . 824--836
Jos L. M. van Dorsselaer and
Michiel E. Hochstenbach and
Henk A. van der Vorst Computing Probabilistic Bounds for
Extreme Eigenvalues of Symmetric
Matrices with the Lanczos Method . . . . 837--852
Zlatko Drmac and
Elizabeth R. Jessup On Accurate Quotient Singular Value
Computation in Floating-Point Arithmetic 853--873
Monique Laurent Polynomial Instances of the Positive
Semidefinite and Euclidean Distance
Matrix Completion Problems . . . . . . . 874--894
J. C. Diaz and
K. Komara Incomplete Multilevel Cholesky
Factorizations . . . . . . . . . . . . . 895--911
George Miminis A Stepwise Approach for the Generalized
Eigenstructure Assignment Problem . . . 912--924
Jun Zhang A Multilevel Dual Reordering Strategy
for Robust Incomplete $ L U $
Factorization of Indefinite Matrices . . 925--947
Yangfeng Su and
Amit Bhaya Convergence of Pseudocontractions and
Applications to Two-stage and
Asynchronous Multisplitting for Singular
$ {M}$-Matrices . . . . . . . . . . . . 948--964
Yuming Chen On Real Solutions of the Equation $
\Phi^t(A) = \frac {1}{n} J_n $ . . . . . 965--970
Adam L. Cohen and
Leiba Rodman and
David P. Stanford Erratum: ``Pointwise and Uniformly
Convergent Sets of Matrices'' . . . . . 971--971
I. S. Duff and
J. Koster On Algorithms For Permuting Large
Entries to the Diagonal of a Sparse
Matrix . . . . . . . . . . . . . . . . . 973--996
Timothy A. Davis and
William W. Hager Multiple-Rank Modifications of a Sparse
Cholesky Factorization . . . . . . . . . 997--1013
Reinhard Nabben On Green's Matrices of Trees . . . . . . 1014--1026
J. M. Peña A Class of $P$-Matrices with
Applications to the Localization of the
Eigenvalues of a Real Matrix . . . . . . 1027--1037
Françoise Tisseur Newton's Method in Floating Point
Arithmetic and Iterative Refinement of
Generalized Eigenvalue Problems . . . . 1038--1057
Ke Chen An Analysis of Sparse Approximate
Inverse Preconditioners for Boundary
Integral Equations . . . . . . . . . . . 1058--1078
Charles R. Johnson and
D. D. Olesky and
P. van den Driessche Successively Ordered Elementary
Bidiagonal Factorization . . . . . . . . 1079--1088
Violeta Migallón and
José Penadés and
Daniel B. Szyld Nonstationary Multisplittings with
General Weighting Matrices . . . . . . . 1089--1094
Liyu Cao and
Howard M. Schwartz A Decomposition Method for Positive
Semidefinite Matrices and Its
Application to Recursive Parameter
Estimation . . . . . . . . . . . . . . . 1095--1111
Sheung Hun Cheng and
Nicholas J. Higham and
Charles S. Kenney and
Alan J. Laub Approximating the Logarithm of a Matrix
to Specified Accuracy . . . . . . . . . 1112--1125
Nicholas J. Higham Evaluating Padé Approximants of the
Matrix Logarithm . . . . . . . . . . . . 1126--1135
Dinh Tuan Pham Joint Approximate Diagonalization of
Positive Definite Hermitian Matrices . . 1136--1152
Elena Y. Bobrovnikova and
Stephen A. Vavasis Accurate Solution of Weighted Least
Squares by Iterative Methods . . . . . . 1153--1174
Konstantin E. Avrachenkov and
Moshe Haviv and
Phil G. Howlett Inversion of Analytic Matrix Functions
That are Singular at the Origin . . . . 1175--1189
Sy-Ming Guu and
Yung-Yih Lur and
Chin-Tzong Pang On Infinite Products of Fuzzy Matrices 1190--1203
Misha E. Kilmer and
Dianne P. O'Leary Choosing Regularization Parameters in
Iterative Methods for Ill-Posed Problems 1204--1221
M. A. Petersen and
A. C. M. Ran Minimal Square Spectral Factors via
Triples . . . . . . . . . . . . . . . . 1222--1244
Zhenyue Zhang and
Hongyuan Zha Structure and Perturbation Analysis of
Truncated SVDs for Column-Partitioned
Matrices . . . . . . . . . . . . . . . . 1245--1262
Cornelis V. M. van der Mee and
André C. M. Ran and
Leiba Rodman Real Hamiltonian Polar Decompositions 1263--1273
G. A. Watson Data Fitting Problems with Bounded
Uncertainties in the Data . . . . . . . 1274--1293
C. Koukouvinos and
M. Mitrouli and
Jennifer Seberry Values of Minors of an Infinite Family
of $ {D}$-Optimal Designs and Their
Application to the Growth Problem . . . 1--14
Patrick R. Amestoy and
Iain S. Duff and
Jean-Yves L'Excellent and
Jacko Koster A Fully Asynchronous Multifrontal Solver
Using Distributed Dynamic Scheduling . . 15--41
Anders Forsgren and
Göran Sporre On Weighted Linear Least-Squares
Problems Related to Interior Methods for
Convex Quadratic Programming . . . . . . 42--56
Amos Ron and
Zuowei Shen and
Kim-Chuan Toh Computing the Sobolev Regularity of
Refinable Functions by the Arnoldi
Method . . . . . . . . . . . . . . . . . 57--76
N. K. Nichols and
J. Kautsky Robust Eigenstructure Assignment in
Quadratic Matrix Polynomials:
Nonsingular Case . . . . . . . . . . . . 77--102
Françoise Tisseur Stability of Structured Hamiltonian
Eigensolvers . . . . . . . . . . . . . . 103--125
R. E. Beardmore The Singularity-Induced Bifurcation and
its Kronecker Normal Form . . . . . . . 126--137
S. Chandrasekaran and
M. Gu and
A. H. Sayed and
K. E. Schubert The Degenerate Bounded
Errors-in-Variables Model . . . . . . . 138--166
Qingtang Jiang Symmetric Paraunitary Matrix Extension
and Parametrization of Symmetric
Orthogonal Multifilter Banks . . . . . . 167--186
Françoise Tisseur and
Nicholas J. Higham Structured Pseudospectra for Polynomial
Eigenvalue Problems, with Applications 187--208
Isaac Sonin and
John Thornton Recursive Algorithm for the
Fundamental/Group Inverse Matrix of a
Markov Chain from an Explicit Formula 209--224
Chun-Hua Guo Nonsymmetric Algebraic Riccati Equations
and Wiener--Hopf Factorization for
$M$-Matrices . . . . . . . . . . . . . . 225--242
Tamara G. Kolda Orthogonal Tensor Decompositions . . . . 243--255
A. Melman The Even-Odd Split Levinson Algorithm
for Toeplitz Systems . . . . . . . . . . 256--270
Barry W. Peyton Minimal Orderings Revisited . . . . . . 271--294
Chun-Hua Guo Convergence Rate of an Iterative Method
for a Nonlinear Matrix Equation . . . . 295--302
Nicholas J. Higham and
Hyun-Min Kim Solving a Quadratic Matrix Equation by
Newton's Method with Exact Line Searches 303--316
Qiya Hu and
Jun Zou An Iterative Method with Variable
Relaxation Parameters for Saddle-Point
Problems . . . . . . . . . . . . . . . . 317--338
Antonio Frangioni and
Stefano Serra Capizzano Spectral Analysis of (Sequences of)
Graph Matrices . . . . . . . . . . . . . 339--348
Marko Huhtanen A Stratification of the Set of Normal
Matrices . . . . . . . . . . . . . . . . 349--367
Adrian S. Lewis and
Hristo S. Sendov Twice Differentiable Spectral Functions 368--386
M. Konstantinov and
V. Mehrmann and
P. Petkov Perturbation Analysis of Hamiltonian
Schur and Block-Schur Forms . . . . . . 387--424
Mario Arioli and
Lucia Baldini A Backward Error Analysis of a Null
Space Algorithm in Sparse Quadratic
Programming . . . . . . . . . . . . . . 425--442
Per Christian Hansen and
Plamen Y. Yalamov Computing Symmetric Rank-Revealing
Decompositions via Triangular
Factorization . . . . . . . . . . . . . 443--458
Josep M. Brunat and
Antonio Montes The Power-Compositions Determinant and
Its Application to Global Optimization 459--471
Philip I. Davies and
Nicholas J. Higham and
Françoise Tisseur Analysis of the Cholesky Method with
Iterative Refinement for Solving the
Symmetric Definite Generalized
Eigenproblem . . . . . . . . . . . . . . 472--493
Marc Van Barel and
Georg Heinig and
Peter Kravanja A Stabilized Superfast Solver for
Nonsymmetric Toeplitz Systems . . . . . 494--510
Fan Ding and
Xingzhi Zhan On the Unitary Orbit of Complex Matrices 511--516
Joachim Rosenthal and
Xiaochang Wang The Multiplicative Inverse Eigenvalue
Problem over an Algebraically Closed
Field . . . . . . . . . . . . . . . . . 517--523
Jonq Juang and
Wen-Wei Lin and
Shih-Feng Shieh Eigenvalue Problems for One-Dimensional
Discrete Schrödinger Operators with
Symmetric Boundary Conditions . . . . . 524--533
Tong Zhang and
Gene H. Golub Rank-One Approximation to High Order
Tensors . . . . . . . . . . . . . . . . 534--550
R. B. Lehoucq Implicitly Restarted Arnoldi Methods and
Subspace Iteration . . . . . . . . . . . 551--562
E. Marques de Sá and
João David Vieira On the Similarity Invariant Polynomials
of Matrices and Principal Submatrices 563--580
Oleg Gusak and
Tuugrul Dayar and
Jean-Michel Fourneau Stochastic Automata Networks and Near
Complete Decomposability . . . . . . . . 581--599
G. W. Stewart A Krylov--Schur Algorithm for Large
Eigenproblems . . . . . . . . . . . . . 601--614
Peter Lancaster and
Panayiotis Psarrakos The Numerical Range of Self-Adjoint
Quadratic Matrix Polynomials . . . . . . 615--631
Salah M. El-Sayed and
André C. M. Ran On an Iteration Method for Solving a
Class of Nonlinear Matrix Equations . . 632--645
J. W. McLean and
H. J. Woerdeman Spectral Factorizations and Sums of
Squares Representations via Semidefinite
Programming . . . . . . . . . . . . . . 646--655
Susana Furtado and
Laura Iglésias and
Fernando C. Silva Products of Real Matrices with
Prescribed Characteristic Polynomials 656--672
C. He and
B. Meini and
N. H. Rhee A Shifted Cyclic Reduction Algorithm for
Quasi-Birth-Death Problems . . . . . . . 673--691
Matthias Bollhöfer and
Yousef Saad A Factored Approximate Inverse
Preconditioner with Pivoting . . . . . . 692--705
Zhenyue Zhang and
Hongyuan Zha and
Horst Simon Low-Rank Approximations with Sparse
Factors I: Basic Algorithms and Error
Analysis . . . . . . . . . . . . . . . . 706--727
D. Noutsos and
P. Vassalos New Band Toeplitz Preconditioners for
Ill-Conditioned Symmetric Positive
Definite Toeplitz Systems . . . . . . . 728--743
Chun-Hua Guo Convergence Analysis of the
Latouche--Ramaswami Algorithm for Null
Recurrent Quasi-Birth-Death Processes 744--760
Jesse L. Barlow More Accurate Bidiagonal Reduction for
Computing the Singular Value
Decomposition . . . . . . . . . . . . . 761--798
Arnold Reusken Approximation of the Determinant of
Large Sparse Symmetric Positive Definite
Matrices . . . . . . . . . . . . . . . . 799--818
Eva Lundström and
Lars Eldén Adaptive Eigenvalue Computations Using
Newton's Method on the Grassmann
Manifold . . . . . . . . . . . . . . . . 819--839
A. Zanna and
H. Z. Munthe-Kaas Generalized Polar Decompositions for the
Approximation of the Matrix Exponential 840--862
Eleftherios Kofidis and
Phillip A. Regalia On the Best Rank-$1$ Approximation of
Higher-Order Supersymmetric Tensors . . 863--884
David Tao and
Mark Yasuda A Spectral Characterization of
Generalized Real Symmetric
Centrosymmetric and Generalized Real
Symmetric Skew-Centrosymmetric Matrices 885--895
Shmuel Friedland Normal Matrices and the Completion
Problem . . . . . . . . . . . . . . . . 896--902
Miroslav T\ocircuma A Note on the $ L D L^T $ Decomposition
of Matrices from Saddle-Point Problems 903--915
Charles R. Johnson and
Christopher J. Hillar Eigenvalues of Words in Two Positive
Definite Letters . . . . . . . . . . . . 916--928
Karen Braman and
Ralph Byers and
Roy Mathias The Multishift $ Q R $ Algorithm. Part
I: Maintaining Well-Focused Shifts and
Level $3$ Performance . . . . . . . . . 929--947
Karen Braman and
Ralph Byers and
Roy Mathias The Multishift $ Q R $ Algorithm. Part
II: Aggressive Early Deflation . . . . . 948--973
N. Del Buono and
L. Lopez Geometric Integration on Manifold of
Square Oblique Rotation Matrices . . . . 974--989
Leng Gangsong and
Zhou GuoBiao Inverse Forms of Hadamard Inequality . . 990--997
Igor Brainman and
Sivan Toledo Nested-Dissection Orderings for Sparse $
L U $ with Partial Pivoting . . . . . . 998--1012
Rupert Lasser and
Sebastian Walcher Error Estimates for Linear Compartmental
Systems . . . . . . . . . . . . . . . . 1013--1024
Moody T. Chu and
Robert E. Funderlic The Centroid Decomposition:
Relationships between Discrete
Variational Decompositions and SVDs . . 1025--1044
Gerhard Freiling and
Volker Mehrmann and
Hongguo Xu Existence, Uniqueness, and
Parametrization of Lagrangian Invariant
Subspaces . . . . . . . . . . . . . . . 1045--1069
Marko Huhtanen and
Rasmus Munk Larsen Exclusion and Inclusion Regions for the
Eigenvalues of a Normal Matrix . . . . . 1070--1091
Marko Huhtanen A Hermitian Lanczos Method for Normal
Matrices . . . . . . . . . . . . . . . . 1092--1108
S. Kirkland On a Question Concerning Condition
Numbers for Markov Chains . . . . . . . 1109--1119
A. H. Sayed and
V. H. Nascimento and
F. A. M. Cipparrone A Regularized Robust Design Criterion
for Uncertain Data . . . . . . . . . . . 1120--1142
Maher Moakher Means and Averaging in the Group of
Rotations . . . . . . . . . . . . . . . 1--16
Lei Li On the Iterative Criterion for
Generalized Diagonally Dominant Matrices 17--24
M. Seetharama Gowda and
Y. Song Some New Results for the Semidefinite
Linear Complementarity Problem . . . . . 25--39
Yair Censor and
Tommy Elfving Block-Iterative Algorithms with
Diagonally Scaled Oblique Projections
for the Linear Feasibility Problem . . . 40--58
Peter Zizler and
Rob A. Zuidwijk and
Keith F. Taylor and
Shigeru Arimoto A Finer Aspect of Eigenvalue
Distribution of Selfadjoint Band
Toeplitz Matrices . . . . . . . . . . . 59--67
Ivo Marek and
Daniel B. Szyld Comparison of Convergence of General
Stationary Iterative Methods for
Singular Matrices . . . . . . . . . . . 68--77
Guo-Lin Li and
Zheng-He Feng Mirrorsymmetric Matrices, Their Basic
Properties, and an Application on
Odd/Even-Mode Decomposition of Symmetric
Multiconductor Transmission Lines . . . 78--90
Michael G. Neubauer and
William Watkins E-optimal Spring Balance Weighing
Designs for $ n \equiv - 1 \ \pmod 4 $
Objects . . . . . . . . . . . . . . . . 91--105
R. E. Beardmore and
R. Laister The Flow of a DAE near a Singular
Equilibrium . . . . . . . . . . . . . . 106--120
Zhi-Hao Cao A Note on Constraint Preconditioning for
Nonsymmetric Indefinite Matrices . . . . 121--125
Chi-Kwong Li and
Roy Mathias Inequalities on Singular Values of Block
Triangular Matrices . . . . . . . . . . 126--131
Peter Arbenz and
Zlatko Drmac On Positive Semidefinite Matrices with
Known Null Space . . . . . . . . . . . . 132--149
Jie Zhou and
Yunmin Zhu and
X. Rong Li and
Zhisheng You Variants of the Greville Formula with
Applications to Exact Recursive Least
Squares . . . . . . . . . . . . . . . . 150--164
Peter Benner and
Ralph Byers and
Volker Mehrmann and
Hongguo Xu Numerical Computation of Deflating
Subspaces of
Skew-Hamiltonian/Hamiltonian Pencils . . 165--190
Matthias Bollhöfer and
Volker Mehrmann Algebraic Multilevel Methods and Sparse
Approximate Inverses . . . . . . . . . . 191--218
Matthias Bollhöfer and
Yousef Saad On the Relations between ILUs and
Factored Approximate Inverses . . . . . 219--237
Andreas Stathopoulos A Case for a Biorthogonal
Jacobi--Davidson Method: Restarting and
Correction Equation . . . . . . . . . . 238--259
Jing-Rebecca Li and
Jacob White Low Rank Solution of Lyapunov Equations 260--280
Tuugrul Dayar and
Franck Quessette Quasi-Birth-and-Death Processes with
Level-Geometric Distribution . . . . . . 281--291
Carla D. Moravitz Martin and
Charles F. Van Loan Product Triangular Systems with Shift 292--301
Jane Cullum and
Tong Zhang Two-Sided Arnoldi and Nonsymmetric
Lanczos Algorithms . . . . . . . . . . . 303--319
Colm O'Cinneide On ``Sluggish Transients'' in Markov
Chains . . . . . . . . . . . . . . . . . 320--333
Bernard C. Levy and
Augusto Ferrante Characterization of Stationary
Discrete-Time Gaussian Reciprocal
Processes over a Finite Interval . . . . 334--355
Qing Lin and
D. D. Olesky and
P. van den Driessche The Distance of Potentially Stable Sign
Patterns to the Unstable Matrices . . . 356--367
M. Rozlozník and
V. Simoncini Krylov Subspace Methods for Saddle Point
Problems with Indefinite Preconditioning 368--391
Michiel E. Hochstenbach and
Bor Plestenjak A Jacobi--Davidson Type Method for a
Right Definite Two-Parameter Eigenvalue
Problem . . . . . . . . . . . . . . . . 392--410
Wen-Wei Lin and
Ji-guang Sun Perturbation Analysis of the Periodic
Discrete-Time Algebraic Riccati Equation 411--438
Oren E. Livne and
Achi Brandt $N$ Roots of the Secular Equation in $
O(N)$ Operations . . . . . . . . . . . . 439--453
S. J. Kirkland and
M. Neumann and
N. Ormes and
J. Xu On the Elasticity of the Perron Root of
a Nonnegative Matrix . . . . . . . . . . 454--464
Winfried K. Grassmann and
Javad Tavakoli A Tandem Queue with a Movable Server: An
Eigenvalue Approach . . . . . . . . . . 465--474
Yi-Zheng Fan and
Jiong-Sheng Li Algebraic Multiplicity of the
Eigenvalues of a Bipartite Tournament
Matrix . . . . . . . . . . . . . . . . . 475--483
Albrecht Böttcher and
Mark Embree and
Lloyd N. Trefethen Piecewise Continuous Toeplitz Matrices
and Operators: Slow Approach to Infinity 484--489
Urho A. Rauhala Array Algebra Expansion of Matrix and
Tensor Calculus: Part 1 . . . . . . . . 490--508
Urho A. Rauhala Array Algebra Expansion of Matrix and
Tensor Calculus: Part 2 . . . . . . . . 509--528
Anshul Gupta Improved Symbolic and Numerical
Factorization Algorithms for Unsymmetric
Sparse Matrices . . . . . . . . . . . . 529--552
Patrick R. Amestoy and
Chiara Puglisi An Unsymmetrized Multifrontal $ L U $
Factorization . . . . . . . . . . . . . 553--569
Si-Ju Kim and
Bryan L. Shader and
Suk-Geun Hwang On Matrices with Signed Null-Spaces . . 570--580
Michael K. Ng and
Daniel Potts Fast Iterative Methods for Sinc Systems 581--598
G. W. Stewart Addendum to ``A Krylov--Schur Algorithm
for Large Eigenproblems'' . . . . . . . 599--601
Zhong-Zhi Bai and
Gene H. Golub and
Michael K. Ng Hermitian and Skew-Hermitian Splitting
Methods for Non-Hermitian Positive
Definite Linear Systems . . . . . . . . 603--626
Yvan Notay Convergence Analysis of Inexact Rayleigh
Quotient Iteration . . . . . . . . . . . 627--644
Moody T. Chu and
Robert J. Plemmons Real-Valued, Low Rank, Circulant
Approximation . . . . . . . . . . . . . 645--659
Victor Y. Pan and
Xinmao Wang Inversion of Displacement Operators . . 660--677
Bernd Silbermann Modified Finite Sections for Toeplitz
Operators and Their Singular Values . . 678--692
Bin Han Computing the Smoothness Exponent of a
Symmetric Multivariate Refinable
Function . . . . . . . . . . . . . . . . 693--714
C. Koukouvinos and
M. Mitrouli and
Jennifer Seberry Values of Minors of an Infinite Family
of $ {D}$-Optimal Designs and Their
Application to the Growth Problem: II 715--727
Caixing Gu and
Linda Patton Commutation Relations for Toeplitz and
Hankel Matrices . . . . . . . . . . . . 728--746
G. Goldberg and
M. Neumann Distribution of Subdominant Eigenvalues
of Matrices with Random Rows . . . . . . 747--761
Tamara G. Kolda A Counterexample to the Possibility of
an Extension of the Eckart--Young
Low-Rank Approximation Theorem for the
Orthogonal Rank Tensor Decomposition . . 762--767
Xiaobai Sun and
Yujuan Bao A Kronecker Product Representation of
the Fast Gauss Transform . . . . . . . . 768--786
Yang Cao and
Linda Petzold A Subspace Error Estimate for Linear
Systems . . . . . . . . . . . . . . . . 787--801
Sang-Yeun Shim and
Yu Chen Least Squares Solution of Matrix
Equation $ {AXB}^* + {CYD}^* = {E} $ . . 802--808
Stuart Clary and
Dale H. Mugler Shifted Fourier Matrices and Their
Tridiagonal Commutors . . . . . . . . . 809--821
Ph. Guillaume and
A. Huard and
C. Le Calvez A Block Constant Approximate Inverse for
Preconditioning Large Linear Systems . . 822--851
Luca Gemignani and
Grazia Lotti Efficient and Stable Solution of
M-Matrix Linear Systems of (Block)
Hessenberg Form . . . . . . . . . . . . 852--876
Françoise Tisseur A Chart of Backward Errors for Singly
and Doubly Structured Eigenvalue
Problems . . . . . . . . . . . . . . . . 877--897
Karlheinz Gröchenig and
Harald Schwab Fast Local Reconstruction Methods for
Nonuniform Sampling in Shift-Invariant
Spaces . . . . . . . . . . . . . . . . . 899--913
Adam Bojanczyk and
Nicholas J. Higham and
Harikrishna Patel Solving the Indefinite Least Squares
Problem by Hyperbolic $ Q R $
Factorization . . . . . . . . . . . . . 914--931
V. Moskvina and
K. M. Schmidt Approximate Projectors in Singular
Spectrum Analysis . . . . . . . . . . . 932--942
M. I. García-Planas and
A. A. Mailybaev Reduction to Versal Deformations of
Matrix Pencils and Matrix Pairs with
Application to Control Theory . . . . . 943--962
Vincent D. Blondel and
Jacques Theys and
Alexander A. Vladimirov An Elementary Counterexample to the
Finiteness Conjecture . . . . . . . . . 963--970
Matthew I. Smith A Schur Algorithm for Computing Matrix
$p$ th Roots . . . . . . . . . . . . . . 971--989
Jia-Yu Shao and
Jin-Ling He and
Hai-Ying Shan Matrices with Special Sign Patterns of
Signed Generalized Inverses . . . . . . 990--1002
Christiane Tretter and
Markus Wagenhofer The Block Numerical Range of an $ n
\times n $ Block Operator Matrix . . . . 1003--1017
Armin Pruessner and
Dianne P. O'Leary Blind Deconvolution Using a Regularized
Structured Total Least Norm Algorithm 1018--1037
Karl Meerbergen The Solution of Parametrized Symmetric
Linear Systems . . . . . . . . . . . . . 1038--1059
Milan Hladnik and
John Holbrook and
Stefano Serra Capizzano Fat Diagonals and Fourier Analysis . . . 1060--1070
Rong-Qing Jia and
Qingtang Jiang Spectral Analysis of the Transition
Operator and Its Applications to
Smoothness Analysis of Wavelets . . . . 1071--1109
V. S. Borisov On Discrete Maximum Principles for
Linear Equation Systems and Monotonicity
of Difference Schemes . . . . . . . . . 1110--1135
Servet Martínez and
Jaime San Martín and
Xiao-Dong Zhang A New Class of Inverse $ {M}$-Matrices
of Tree-Like Type . . . . . . . . . . . 1136--1148
Eric T. Chung and
Jun Zou The Eigenvalues and Eigenspaces of Some
Discrete Div- and Curl-Related Operators 1149--1160
Chun-Hua Guo Comments on a Shifted Cyclic Reduction
Algorithm for Quasi-Birth-Death Problems 1161--1166
Antonia Vecchio A Bound for the Inverse of a Lower
Triangular Toeplitz Matrix . . . . . . . 1167--1174
Luca Dieci and
Luciano Lopez Lyapunov Exponents of Systems Evolving
on Quadratic Groups . . . . . . . . . . 1175--1185
A. N. Malyshev A Unified Theory of Conditioning for
Linear Least Squares and Tikhonov
Regularization Solutions . . . . . . . . 1186--1196
Siegfried M. Rump Structured Perturbations Part I:
Normwise Distances . . . . . . . . . . . 1--30
Siegfried M. Rump Structured Perturbations Part II:
Componentwise Distances . . . . . . . . 31--56
Y. Genin and
Y. Hachez and
Yu. Nesterov and
P. Van Dooren Optimization Problems over Positive
Pseudopolynomial Matrices . . . . . . . 57--79
J. V. Burke and
A. S. Lewis and
M. L. Overton Optimization and Pseudospectra, with
Applications to Robust Stability . . . . 80--104
Z. D. Bai and
Baiqi Miao and
Jian-feng Yao Convergence Rates of Spectral
Distributions of Large Sample Covariance
Matrices . . . . . . . . . . . . . . . . 105--127
J. E. Castillo and
R. D. Grone A Matrix Analysis Approach to
Higher-Order Approximations for
Divergence and Gradients Satisfying a
Global Conservation Law . . . . . . . . 128--142
John R. Gilbert and
Laura Grigori A Note on the Column Elimination Tree 143--151
Stefano Serra Capizzano and
Cristina Tablino Possio Superlinear Preconditioners for Finite
Differences Linear Systems . . . . . . . 152--164
Peg Howland and
Moongu Jeon and
Haesun Park Structure Preserving Dimension Reduction
for Clustered Text Data Based on the
Generalized Singular Value Decomposition 165--179
Raphael Loewy and
Volker Mehrmann A Note on the Symmetric Recursive
Inverse Eigenvalue Problem . . . . . . . 180--187
Zhenyue Zhang and
Yushan Huang A Projection Method for Least Squares
Problems with a Quadratic Equality
Constraint . . . . . . . . . . . . . . . 188--212
André Klein and
Peter Spreij Some Results on Vandermonde Matrices
with an Application to Time Series
Analysis . . . . . . . . . . . . . . . . 213--223
P. Ciarlet, Jr. and
Jianguo Huang and
Jun Zou Some Observations on Generalized
Saddle-Point Problems . . . . . . . . . 224--236
Jiri Rohn Solvability of Systems of Linear
Interval Equations . . . . . . . . . . . 237--245
Zhongxiao Jia and
Datian Niu An Implicitly Restarted Refined
Bidiagonalization Lanczos Method for
Computing a Partial Singular Value
Decomposition . . . . . . . . . . . . . 246--265
Hansjörg Linden The Quadratic Numerical Range and the
Location of Zeros of Polynomials . . . . 266--284
C. R. Johnson and
D. D. Olesky and
P. van den Driessche Matrix Classes That Generate all
Matrices with Positive Determinant . . . 285--294
Simone Severini On the Digraph of a Unitary Matrix . . . 295--300
Froilán M. Dopico and
Juan M. Molera and
Julio Moro An Orthogonal High Relative Accuracy
Algorithm for the Symmetric Eigenproblem 301--351
Charles R. Johnson and
António Leal Duarte and
Carlos M. Saiago The Parter--Wiener Theorem: Refinement
and Generalization . . . . . . . . . . . 352--361
Wen Li and
Weiwei Sun New Perturbation Bounds for Unitary
Polar Factors . . . . . . . . . . . . . 362--372
S. Chandrasekaran and
M. Gu Fast and Stable Algorithms for Banded
Plus Semiseparable Systems of Linear
Equations . . . . . . . . . . . . . . . 373--384
Ming Gu and
Robert Guzzo and
Xue-bin Chi and
Xing-Qin Cao A Stable Divide and Conquer Algorithm
for the Unitary Eigenproblem . . . . . . 385--404
Ren-Cang Li and
Qiang Ye A Krylov Subspace Method for Quadratic
Matrix Polynomials with Application to
Constrained Least Squares Problems . . . 405--428
Desmond J. Higham A Matrix Perturbation View of the Small
World Phenomenon . . . . . . . . . . . . 429--444
Y. Chahlaoui and
K. Gallivan and
P. Van Dooren Recursive Calculation of Dominant
Singular Subspaces . . . . . . . . . . . 445--463
Philip I. Davies and
Nicholas J. Higham A Schur--Parlett Algorithm for Computing
Matrix Functions . . . . . . . . . . . . 464--485
Yuan-Bei Deng and
Xi-Yan Hu and
Lei Zhang Least Squares Solution of $ B X A^T = T
$ over Symmetric, Skew-Symmetric, and
Positive Semidefinite $X$ . . . . . . . 486--494
Julio Moro and
Froilán M. Dopico Low Rank Perturbation of Jordan
Structure . . . . . . . . . . . . . . . 495--506
Marc Artzrouni The Local Coefficient of Ergodicity of a
Nonnegative Matrix . . . . . . . . . . . 507--516
Qiuhui Chen and
Charles A. Micchelli and
Silong Peng and
Yuesheng Xu Multivariate Filter Banks Having Matrix
Factorizations . . . . . . . . . . . . . 517--531
Radka Turcajová An Algorithm for the Construction of
Symmetric Orthogonal Multiwavelets . . . 532--550
Eric King-wah Chu Perturbation of Eigenvalues for Matrix
Polynomials via The Bauer--Fike Theorems 551--573
Stephen G. Walker On Recent Cheeger-Type Bounds for
Nonmaximal Eigenvalues Applied to
Positive Matrices . . . . . . . . . . . 574--581
Leslie V. Foster Solving Rank-Deficient and Ill-posed
Problems Using $ U T V $ and $ Q R $
Factorizations . . . . . . . . . . . . . 582--600
Mark Yasuda Spectral Characterizations for Hermitian
Centrosymmetric $K$-Matrices and
Hermitian Skew-Centrosymmetric
$K$-Matrices . . . . . . . . . . . . . . 601--605
P. Lancaster and
A. S. Markus and
F. Zhou Perturbation Theory for Analytic Matrix
Functions: The Semisimple Case . . . . . 606--626
Xiao-Qing Jin and
Yi-Min Wei and
Wei Xu A Stability Property of T. Chan's
Preconditioner . . . . . . . . . . . . . 627--629
Markus Baumann and
Peter Fleischmann and
Otto Mutzbauer Double Ordering and Fill-In for the $ L
U $ Factorization . . . . . . . . . . . 630--641
Judith M. Ford An Improved Discrete Wavelet Transform
Preconditioner for Dense Matrix Problems 642--661
Rajendra Bhatia and
Ludwig Elsner Higher Order Logarithmic Derivatives of
Matrices in the Spectral Norm . . . . . 662--668
Michael Stewart A Superfast Toeplitz Solver with
Improved Numerical Stability . . . . . . 669--693
Erik G. Boman and
Bruce Hendrickson Support Theory for Preconditioning . . . 694--717
Catherine Elizabeth Powell and
David Silvester Optimal Preconditioning for
Raviart--Thomas Mixed Formulation of
Second-Order Elliptic Problems . . . . . 718--738
Sy-Ming Guu and
Chin-Tzong Pang On the Convergence to Zero of Infinite
Products of Interval Matrices . . . . . 739--751
Xiao-Dong Zhang The Equality Cases for the Inequalities
of Fischer, Oppenheim, and Ando for
General $ {M}$-Matrices . . . . . . . . 752--765
Houduo Qi and
Xiaoqi Yang Semismoothness of Spectral Functions . . 766--783
David K. Maslen and
Michael E. Orrison and
Daniel N. Rockmore Computing Isotypic Projections with the
Lanczos Iteration . . . . . . . . . . . 784--803
Timo Eirola and
Marko Huhtanen and
Jan von Pfaler Solution Methods for $ \mathbb {R}
$-Linear Problems in $ \mathbb {C}^n $ 804--828
James G. Nagy and
Michael K. Ng and
Lisa Perrone Kronecker Product Approximations for
Image Restoration with Reflexive
Boundary Conditions . . . . . . . . . . 829--841
Georg Heinig and
Karla Rost New Fast Algorithms for
Toeplitz-Plus-Hankel Matrices . . . . . 842--857
Inderjit S. Dhillon and
Beresford N. Parlett Orthogonal Eigenvectors and Relative
Gaps . . . . . . . . . . . . . . . . . . 858--899
Charles R. Johnson and
D. D. Olesky and
P. van den Driessche Erratum: ``Successively Ordered
Elementary Bidiagonal Factorization'' 900--900
Zhenyue Zhang and
Hongyuan Zha and
Horst Simon Low-Rank Approximations with Sparse
Factors II: Penalized Methods with
Discrete Newton-Like Iterations . . . . 901--920
Raghib Abu-Saris and
Wajdi Ahmad Generalized Exponential Vandermonde
Determinant and Hermite Multipoint
Discrete Boundary Value Problem . . . . 921--929
Thomas Huckle and
Stefano Serra-Capizzano The Spectra of Preconditioned Toeplitz
Matrix Sequences Can Have Gaps . . . . . 930--946
A. Melman Computation of the Smallest Even and Odd
Eigenvalues of a Symmetric
Positive-Definite Toeplitz Matrix . . . 947--963
Christian Mehl Jacobi-like Algorithms for the
Indefinite Generalized Hermitian
Eigenvalue Problem . . . . . . . . . . . 964--985
M. Gassó and
Juan R. Torregrosa A Totally Positive Factorization of
Rectangular Matrices by the Neville
Elimination . . . . . . . . . . . . . . 986--994
Moody T. Chu and
Yuen-Cheng Kuo and
Wen-Wei Lin On Inverse Quadratic Eigenvalue Problems
with Partially Prescribed Eigenstructure 995--1020
Froilán M. Dopico and
Julio Moro A Note on Multiplicative Backward Errors
of Accurate SVD Algorithms . . . . . . . 1021--1031
K.-H. Förster and
B. Nagy Connections between Realizations of a
Transfer Function . . . . . . . . . . . 1032--1045
Yuen-Cheng Kuo and
Wen-Wei Lin and
Shu-Fang Xu Regularization of Linear Discrete-Time
Periodic Descriptor Systems by
Derivative and Proportional State
Feedback . . . . . . . . . . . . . . . . 1046--1073
Christopher Beattie and
Mark Embree and
John Rossi Convergence of Restarted Krylov
Subspaces to Invariant Subspaces . . . . 1074--1109
Arieh Iserles and
Antonella Zanna On the Spectra of Certain Matrices
Generated by Involutory Automorphisms 1110--1123
J. William Helton and
Scott McCullough Convex Noncommutative Polynomials Have
Degree Two or Less . . . . . . . . . . . 1124--1139
Yik-Hoi Au-Yeung and
Chi-Kwong Li and
Leiba Rodman $ {H}$-Unitary and Lorentz Matrices: a
Review . . . . . . . . . . . . . . . . . 1140--1162
Luc Giraud and
Serge Gratton and
Julien Langou A Rank-$k$ Update Procedure for
Reorthogonalizing the Orthogonal Factor
from Modified Gram--Schmidt . . . . . . 1163--1177
Nicholas J. Higham and
D. Steven Mackey and
Niloufer Mackey and
Françoise Tisseur Computing the Polar Decomposition and
the Matrix Sign Decomposition in Matrix
Groups . . . . . . . . . . . . . . . . . 1178--1192
Ji-Guang Sun Backward Perturbation Analysis of the
Periodic Discrete-Time Algebraic Riccati
Equation . . . . . . . . . . . . . . . . 1--19
Michele Benzi and
Gene H. Golub A Preconditioner for Generalized Saddle
Point Problems . . . . . . . . . . . . . 20--41
M. Kleinsteuber and
U. Helmke and
K. Huper Jacobi's Algorithm on Compact Lie
Algebras . . . . . . . . . . . . . . . . 42--69
P.-A. Absil and
R. Sepulchre and
P. Van Dooren and
R. Mahony Cubically Convergent Iterations for
Invariant Subspace Computation . . . . . 70--96
Bin Han and
Qun Mo Splitting a Matrix of Laurent
Polynomials with Symmetry and its
Application to Symmetric Framelet Filter
Banks . . . . . . . . . . . . . . . . . 97--124
Jasper van den Eshof and
Gerard L. G. Sleijpen Inexact Krylov Subspace Methods for
Linear Systems . . . . . . . . . . . . . 125--153
Leonid Knizhnerman Stability Estimates on the Jacobi and
Unitary Hessenberg Inverse Eigenvalue
Problems . . . . . . . . . . . . . . . . 154--169
S. J. Kirkland and
M. Neumann and
J. Xu Convexity and Elasticity of the Growth
Rate in Size-Classified Population
Models . . . . . . . . . . . . . . . . . 170--185
Antonio Aric\`o and
M. Donatelli and
S. Serra Capizzano V-cycle Optimal Convergence for Certain
(Multilevel) Structured Linear Systems 186--214
Françoise Tisseur Tridiagonal-Diagonal Reduction of
Symmetric Indefinite Pairs . . . . . . . 215--232
J. Liesen and
Z. Strakos Convergence of GMRES for Tridiagonal
Toeplitz Matrices . . . . . . . . . . . 233--251
Hung-Yuan Fan and
Wen-Wei Lin and
Paul Van Dooren Normwise Scaling of Second Order
Polynomial Matrices . . . . . . . . . . 252--256
T. Britz and
J. J. McDonald and
D. D. Olesky and
P. van den Driessche Minimal Spectrally Arbitrary Sign
Patterns . . . . . . . . . . . . . . . . 257--271
Jérôme Malick A Dual Approach to Semidefinite
Least-Squares Problems . . . . . . . . . 272--284
Fasma Diele and
Teresa Laudadio and
Nicola Mastronardi On Some Inverse Eigenvalue Problems with
Toeplitz-Related Structure . . . . . . . 285--294
Lieven De Lathauwer and
Bart De Moor and
Joos Vandewalle Computation of the Canonical
Decomposition by Means of a Simultaneous
Generalized Schur Decomposition . . . . 295--327
K. Gallivan and
A. Vandendorpe and
P. Van Dooren Model Reduction of MIMO Systems via
Tangential Interpolation . . . . . . . . 328--349
J. V. Burke and
A. S. Lewis and
M. L. Overton Pseudospectral Components and the
Distance to Uncontrollability . . . . . 350--361
Beatrice Meini The Matrix Square Root from a New
Functional Perspective: Theoretical
Results and Computational Issues . . . . 362--376
Valeria Simoncini and
Michele Benzi Spectral Properties of the Hermitian and
Skew-Hermitian Splitting Preconditioner
for Saddle Point Problems . . . . . . . 377--389
Charles R. Johnson and
Brian D. Sutton Hermitian Matrices, Eigenvalue
Multiplicities, and Eigenvector
Components . . . . . . . . . . . . . . . 390--399
Gudbjörn F. Jónsson and
Stephen Vavasis Solving Polynomials with Small Leading
Coefficients . . . . . . . . . . . . . . 400--414
Ricardo C. L. F. Oliveira and
Pedro L. D. Peres A Simple and Less Conservative Test for
$ \mathbb {D} $-Stability . . . . . . . 415--425
Jean-Marc Aza\"\is and
Mario Wschebor Upper and Lower Bounds for the Tails of
the Distribution of the Condition Number
of a Gaussian Matrix . . . . . . . . . . 426--440
T. Ratnarajah and
R. Vaillancourt and
M. Alvo Eigenvalues and Condition Numbers of
Complex Random Matrices . . . . . . . . 441--456
Rosemary A. Renaut and
Hongbin Guo Efficient Algorithms for Solution of
Regularized Total Least Squares . . . . 457--476
Michiel E. Hochstenbach and
Tomaz Kosir and
Bor Plestenjak A Jacobi--Davidson Type Method for the
Two-Parameter Eigenvalue Problem . . . . 477--497
U. B. Holz and
G. H. Golub and
K. H. Law A Subspace Approximation Method for the
Quadratic Eigenvalue Problem . . . . . . 498--521
Yvan Notay Is Jacobi--Davidson Faster than
Davidson? . . . . . . . . . . . . . . . 522--543
Patrick R. Amestoy and
Iain S. Duff and
Christof Vömel Task Scheduling in an Asynchronous
Distributed Memory Multifrontal Solver 544--565
Katarina Blom and
Axel Ruhe A Krylov Subspace Method for Information
Retrieval . . . . . . . . . . . . . . . 566--582
K. Tunyan and
K. Egiazarian and
A. Tuniev and
J. Astola An Efficient Approach to the Linear
Least Squares Problem . . . . . . . . . 583--598
Benedikt Grosser and
Bruno Lang On Symmetric Eigenproblems Induced by
the Bidiagonal SVD . . . . . . . . . . . 599--620
Timothy A. Davis and
William W. Hager Row Modifications of a Sparse Cholesky
Factorization . . . . . . . . . . . . . 621--639
Zhaojun Bai and
Yangfeng Su SOAR: a Second-order Arnoldi Method for
the Solution of the Quadratic Eigenvalue
Problem . . . . . . . . . . . . . . . . 640--659
Amina Bouras and
Valérie Frayssé Inexact Matrix-Vector Products in Krylov
Methods for Solving Linear Systems: a
Relaxation Strategy . . . . . . . . . . 660--678
Lin-Zhang Lu Solution Form and Simple Iteration of a
Nonsymmetric Algebraic Riccati Equation
Arising in Transport Theory . . . . . . 679--685
Stanley C. Eisenstat and
Joseph W. H. Liu The Theory of Elimination Trees for
Sparse Unsymmetric Matrices . . . . . . 686--705
Thomas Kailath and
Vadim Olshevsky Displacement Structure Approach to
Discrete-Trigonometric-Transform Based
Preconditioners of G. Strang Type and of
T. Chan Type . . . . . . . . . . . . . . 706--734
Maher Moakher A Differential Geometric Approach to the
Geometric Mean of Symmetric
Positive-Definite Matrices . . . . . . . 735--747
William F. Trench Characterization and Properties of $ (R,
S) $-Symmetric, $ (R, S) $-Skew
Symmetric, and $ (R, S) $-Conjugate
Matrices . . . . . . . . . . . . . . . . 748--757
Leonid Gurvits and
Leiba Rodman On Matrix Polynomials with Real Roots 758--764
Daniela Calvetti and
Sun-Mi Kim and
Lothar Reichel Quadrature Rules Based on the Arnoldi
Process . . . . . . . . . . . . . . . . 765--781
S. Helsen and
A. B. J. Kuijlaars and
M. Van Barel Convergence of the Isometric Arnoldi
Process . . . . . . . . . . . . . . . . 782--809
Marc Van Barel and
Dario Fasino and
Luca Gemignani and
Nicola Mastronardi Orthogonal Rational Functions and
Structured Matrices . . . . . . . . . . 810--829
R. Alam and
S. Bora On Stable Eigendecompositions of
Matrices . . . . . . . . . . . . . . . . 830--848
Nicholas J. Higham and
D. Steven Mackey and
Niloufer Mackey and
Françoise Tisseur Functions Preserving Matrix Groups and
Iterations for the Matrix Square Root 849--877
Roger B. Sidje and
K. Burrage $ Q R T $: a $ Q R $-Based
Tridiagonalization Algorithm for
Nonsymmetric Matrices . . . . . . . . . 878--900
Leiba Rodman Invariant Subspaces of Skew-Adjoint
Matrices in Skew-Symmetric Inner
Products . . . . . . . . . . . . . . . . 901--907
J. M. Peña Exclusion and Inclusion Intervals for
the Real Eigenvalues of Positive
Matrices . . . . . . . . . . . . . . . . 908--917
T. Y. Li and
Zhonggang Zeng A Rank-Revealing Method with Updating,
Downdating, and Applications . . . . . . 918--946
Daniel Kressner Perturbation Bounds for Isotropic
Invariant Subspaces of Skew-Hamiltonian
Matrices . . . . . . . . . . . . . . . . 947--961
A. H. Baker and
E. R. Jessup and
T. Manteuffel A Technique for Accelerating the
Convergence of Restarted GMRES . . . . . 962--984
T. Londre and
N. H. Rhee Numerical Stability of the Parallel
Jacobi Method . . . . . . . . . . . . . 985--1000
Lothar Reichel and
Qiang Ye Breakdown-free GMRES for Singular
Systems . . . . . . . . . . . . . . . . 1001--1021
Beresford N. Parlett A Bidiagonal Matrix Determines Its
Hyperbolic SVD to Varied Relative
Accuracy . . . . . . . . . . . . . . . . 1022--1057
Hongguo Xu A Numerical Method for Computing an
SVD-like Decomposition . . . . . . . . . 1058--1082
Ivan Markovsky and
Sabine Van Huffel and
Rik Pintelon Block-Toeplitz/Hankel Structured Total
Least Squares . . . . . . . . . . . . . 1083--1099
Zheng-Jian Bai The Inverse Eigenproblem of
Centrosymmetric Matrices with a
Submatrix Constraint and Its
Approximation . . . . . . . . . . . . . 1100--1114
Zhenyue Zhang and
Jing Wang and
Min Fang Necessary and Sufficient Conditions for
the Existence of Positive Definite
Solutions to the Symmetric Recursive
Inverse Eigenvalue Problem . . . . . . . 1115--1131
C. V. M. van der Mee and
S. Seatzu A Method for Generating Infinite
Positive Self-adjoint Test Matrices and
Riesz Bases . . . . . . . . . . . . . . 1132--1149
Victoria E. Howle and
Stephen A. Vavasis An Iterative Method for Solving
Complex-Symmetric Systems Arising in
Electrical Power Modeling . . . . . . . 1150--1178
Nicholas J. Higham The Scaling and Squaring Method for the
Matrix Exponential Revisited . . . . . . 1179--1193
Plamen Koev Accurate Eigenvalues and SVDs of Totally
Nonnegative Matrices . . . . . . . . . . 1--23
Wen-Yang Lin and
Chuen-Liang Chen On Optimal Reorderings of Sparse
Matrices for Parallel Cholesky
Factorizations . . . . . . . . . . . . . 24--45
M. Chu and
N. Del Buono and
L. Lopez and
T. Politi On the Low-Rank Approximation of Data on
the Unit Sphere . . . . . . . . . . . . 46--60
Inderjit S. Dhillon and
Robert W. Heath, Jr. and
Mátyás A. Sustik and
Joel A. Tropp Generalized Finite Algorithms for
Constructing Hermitian Matrices with
Prescribed Diagonal and Spectrum . . . . 61--71
Yimin Wei and
Xiezhang Li and
Fanbin Bu A Perturbation Bound of the Drazin
Inverse of a Matrix by Separation of
Simple Invariant Subspaces . . . . . . . 72--81
Stefano Serra-Capizzano and
Daniele Bertaccini and
Gene H. Golub How to Deduce a Proper Eigenvalue
Cluster from a Proper Singular Value
Cluster in the Nonnormal Case . . . . . 82--86
Cheong Hee Park and
Haesun Park Nonlinear Discriminant Analysis Using
Kernel Functions and the Generalized
Singular Value Decomposition . . . . . . 87--102
Rajendra Bhatia and
Driss Drissi Generalized Lyapunov Equations and
Positive Definite Functions . . . . . . 103--114
Peter Lancaster and
Panayiotis Psarrakos On the Pseudospectra of Matrix
Polynomials . . . . . . . . . . . . . . 115--129
C. M. da Fonseca Interlacing Properties for Hermitian
Matrices Whose Graph is a Given Tree . . 130--141
James Demmel and
Plamen Koev The Accurate and Efficient Solution of a
Totally Positive Generalized Vandermonde
Linear System . . . . . . . . . . . . . 142--152
Dario A. Bini and
Luca Gemignani and
Françoise Tisseur The Ehrlich--Aberth Method for the
Nonsymmetric Tridiagonal Eigenvalue
Problem . . . . . . . . . . . . . . . . 153--175
M. Van Barel and
R. Vandebril and
N. Mastronardi An Orthogonal Similarity Reduction of a
Matrix into Semiseparable Form . . . . . 176--197
Jesse L. Barlow and
Hasan Erbay and
Ivan Slapnicar An Alternative Algorithm for the
Refinement of ULV Decompositions . . . . 198--211
Kenneth S. Berenhaut and
Daniel C. Morton and
Preston T. Fletcher Bounds for Inverses of Triangular
Toeplitz Matrices . . . . . . . . . . . 212--217
Fred Greensite Inverse Problems with $ I \otimes A $
Kronecker Structure . . . . . . . . . . 218--237
Amir Beck and
Aharon Ben-Tal A Global Solution for the Structured
Total Least Squares Problem with Block
Circulant Matrices . . . . . . . . . . . 238--255
Vincent D. Blondel and
Yurii Nesterov Computationally Efficient Approximations
of the Joint Spectral Radius . . . . . . 256--272
A. Rogozhin The Singular Value Behavior of the
Finite Sections of Block Toeplitz
Operators . . . . . . . . . . . . . . . 273--293
Zhong-Zhi Zhang and
Xi-Yan Hu and
Lei Zhang On the Hermitian-Generalized Hamiltonian
Solutions of Linear Matrix Equations . . 294--303
Stefano Serra-Capizzano Jordan Canonical Form of the Google
Matrix: a Potential Contribution to the
PageRank Computation . . . . . . . . . . 305--312
Iain S. Duff and
Stéphane Pralet Strategies for Scaling and Pivoting for
Sparse Symmetric Indefinite Problems . . 313--340
S. Chandrasekaran and
P. Dewilde and
M. Gu and
T. Pals and
X. Sun and
A.-J. van der Veen and
D. White Some Fast Algorithms for Sequentially
Semiseparable Representations . . . . . 341--364
C. W. Scherer Relaxations for Robust Linear Matrix
Inequality Problems with Verifications
for Exactness . . . . . . . . . . . . . 365--395
Tugrul Dayar and
Nail Akar Computing Moments of First Passage Times
to a Subset of States in Markov Chains 396--412
Begoña Cantó and
Carmen Coll and
Elena Sánchez Drazin Inverse and Periodic Collection
of Matrices . . . . . . . . . . . . . . 413--423
Ren-Cang Li Relative Perturbation Bounds for
Positive Polar Factors of Graded
Matrices . . . . . . . . . . . . . . . . 424--433
Shmuel Friedland A New Approach to Generalized Singular
Value Decomposition . . . . . . . . . . 434--444
Rafael Bru and
Francisco Pedroche and
Daniel B. Szyld Additive Schwarz Iterations for Markov
Chains . . . . . . . . . . . . . . . . . 445--458
Kevin A. O'Neil Critical Points of the Singular Value
Decomposition . . . . . . . . . . . . . 459--473
Cheong Hee Park and
Haesun Park A Relationship between Linear
Discriminant Analysis and the
Generalized Minimum Squared Error
Solution . . . . . . . . . . . . . . . . 474--492
G. W. Stewart Error Analysis of the
Quasi-Gram--Schmidt Algorithm . . . . . 493--506
Li Qiu and
Yanxia Zhang and
Chi-Kwong Li Unitarily Invariant Metrics on the
Grassmann Space . . . . . . . . . . . . 507--531
Stephen Boyd and
Lin Xiao Least-Squares Covariance Matrix
Adjustment . . . . . . . . . . . . . . . 532--546
Alan Edelman and
Brian D. Sutton Tails of Condition Number Distributions 547--560
Froilán M. Dopico and
Juan M. Molera Perturbation Theory for Factorizations
of $ L U $ Type through Series
Expansions . . . . . . . . . . . . . . . 561--581
Gregory Boutry and
Michael Elad and
Gene H. Golub and
Peyman Milanfar The Generalized Eigenvalue Problem for
Nonsquare Pencils Using a Minimal
Perturbation Approach . . . . . . . . . 582--601
Zizhong Chen and
Jack J. Dongarra Condition Numbers of Gaussian Random
Matrices . . . . . . . . . . . . . . . . 603--620
Gema M. Diaz-Toca and
Laureano Gonzalez-Vega and
Henri Lombardi Generalizing Cramer's Rule: Solving
Uniformly Linear Systems of Equations 621--637
Yi Lu and
Clifford M. Hurvich On the Complexity of the Preconditioned
Conjugate Gradient Algorithm for Solving
Toeplitz Systems with a Fisher--Hartwig
Singularity . . . . . . . . . . . . . . 638--653
Masaya Matsuura Relations Among the Minimum Norm
Coefficients for Degenerate
Nonstationary Flows . . . . . . . . . . 654--664
Jianzhou Liu and
Fuzhen Zhang Disc Separation of the Schur Complement
of Diagonally Dominant Matrices and
Determinantal Bounds . . . . . . . . . . 665--674
An-Ping Liao and
Zhong-Zhi Bai and
Yuan Lei Best Approximate Solution of Matrix
Equation $ A X B + C Y D = E $ . . . . . 675--688
Hans-Robert Arndt and
Günter Mayer New Criteria for the Semiconvergence of
Interval Matrices . . . . . . . . . . . 689--711
Dénes Petz and
Róbert Temesi Means of Positive Numbers and Matrices 712--720
N. Guglielmi and
F. Wirth and
M. Zennaro Complex Polytope Extremality Results for
Families of Matrices . . . . . . . . . . 721--743
Marzio Sala and
John N. Shadid and
Ray S. Tuminaro An Improved Convergence Bound for
Aggregation-Based Domain Decomposition
Preconditioners . . . . . . . . . . . . 744--756
Robert Hartwig and
Xiezhang Li and
Yimin Wei Representations for the Drazin Inverse
of a $ 2 \times 2 $ Block Matrix . . . . 757--771
B. Beckermann and
S. A. Goreinov and
E. E. Tyrtyshnikov Some Remarks on the Elman Estimate for
GMRES . . . . . . . . . . . . . . . . . 772--778
Gene H. Golub and
Chen Greif and
James M. Varah An Algebraic Analysis of a Block
Diagonal Preconditioner for Saddle Point
Systems . . . . . . . . . . . . . . . . 779--792
Chi-Kwong Li and
Hugo J. Woerdeman A Lower Bound on the C-Numerical Radius
of Nilpotent Matrices Appearing in
Coherent Spectroscopy . . . . . . . . . 793--800
Gareth I. Hargreaves Computing the Condition Number of
Tridiagonal and
Diagonal-Plus-Semiseparable Matrices in
Linear Time . . . . . . . . . . . . . . 801--820
D. Steven Mackey and
Niloufer Mackey and
Françoise Tisseur Structured Factorizations in Scalar
Product Spaces . . . . . . . . . . . . . 821--850
Xingzhi Zhan Extremal Eigenvalues of Real Symmetric
Matrices with Entries in an Interval . . 851--860
Christopher C. Paige and
Zdenek Strakos Core Problems in Linear Algebraic
Systems . . . . . . . . . . . . . . . . 861--875
Michael Stewart and
Paul Van Dooren On the Factorization of Hyperbolic and
Unitary Transformations into Rotations 876--890
Wolfgang Wülling On Stabilization and Convergence of
Clustered Ritz Values in the Lanczos
Method . . . . . . . . . . . . . . . . . 891--908
Mario Bebendorf Approximate Inverse Preconditioning of
Finite Element Discretizations of
Elliptic Operators with Nonsmooth
Coefficients . . . . . . . . . . . . . . 909--929
Marshall Bern and
John R. Gilbert and
Bruce Hendrickson and
Nhat Nguyen and
Sivan Toledo Support-Graph Preconditioners . . . . . 930--951
Ilse C. F. Ipsen and
Steve Kirkland Convergence Analysis of a PageRank
Updating Algorithm by Langville and
Meyer . . . . . . . . . . . . . . . . . 952--967
Amy N. Langville and
Carl D. Meyer Updating Markov Chains with an Eye on
Google's PageRank . . . . . . . . . . . 968--987
S. K. Neogy and
A. K. Das Some Properties of Generalized Positive
Subdefinite Matrices . . . . . . . . . . 988--995
Yvan Notay Aggregation-Based Algebraic Multilevel
Preconditioning . . . . . . . . . . . . 998--1018
Hans De Sterck and
Ulrike Meier Yang and
Jeffrey J. Heys Reducing Complexity in Parallel
Algebraic Multigrid Preconditioners . . 1019--1039
Panayot S. Vassilevski and
Ludmil T. Zikatanov Multiple Vector Preserving Interpolation
Mappings in Algebraic Multigrid . . . . 1040--1055
Robert Bridson and
Chen Greif A Multipreconditioned Conjugate Gradient
Algorithm . . . . . . . . . . . . . . . 1056--1068
Ingyu Lee and
Padma Raghavan and
Esmond G. Ng Effective Preconditioning through
Ordering Interleaved with Incomplete
Factorization . . . . . . . . . . . . . 1069--1088
L. Giraud and
S. Gratton On the Sensitivity of Some Spectral
Preconditioners . . . . . . . . . . . . 1089--1105
Michele Benzi and
Michael K. Ng Preconditioned Iterative Methods for
Weighted Toeplitz Least Squares Problems 1106--1124
Mike A. Botchev and
Gene H. Golub A Class of Nonsymmetric Preconditioners
for Saddle Point Problems . . . . . . . 1125--1149
Randolph E. Bank and
Justin W. L. Wan and
Zhenpeng Qu Kernel Preserving Multigrid Methods for
Convection-Diffusion Equations . . . . . 1150--1171
Sabine Le Borne and
Lars Grasedyck $H$-matrix Preconditioners in
Convection-Dominated Problems . . . . . 1172--1183
Johnathan M. Bardsley and
James G. Nagy Covariance-Preconditioned Iterative
Methods for Nonnegatively Constrained
Astronomical Imaging . . . . . . . . . . 1184--1197
M. Gasca and
J. M. Peña Characterizations and Decompositions of
Almost Strictly Positive Matrices . . . 1--8
Julio Benítez and
Néstor Thome $k$-Group Periodic Matrices . . . . . . 9--25
Wen-Wei Lin and
Shu-Fang Xu Convergence Analysis of
Structure-Preserving Doubling Algorithms
for Riccati-Type Matrix Equations . . . 26--39
Michael Stewart An Error Analysis of a Unitary
Hessenberg QR Algorithm . . . . . . . . 40--67
Shaun M. Fallat and
Allen Herman and
Michael I. Gekhtman and
Charles R. Johnson Compressions of Totally Positive
Matrices . . . . . . . . . . . . . . . . 68--80
Susana Furtado and
Charles R. Johnson Perturbation of Matrices Diagonalizable
under Congruence . . . . . . . . . . . . 81--88
A. C. M. Ran and
M. C. B. Reurings and
L. Rodman A Perturbation Analysis for Nonlinear
Selfadjoint Operator Equations . . . . . 89--104
Linda Kaufman Eigenvalue Problems in Fiber Optic
Design . . . . . . . . . . . . . . . . . 105--117
Antonia M. Delgado and
Jeffrey S. Geronimo and
Plamen Iliev and
Francisco Marcellán Two variable orthogonal polynomials and
structured matrices . . . . . . . . . . 118--147
Shreemayee Bora and
Volker Mehrmann Linear Perturbation Theory for
Structured Matrix Pencils Arising in
Control Theory . . . . . . . . . . . . . 148--169
H. Sue Dollar and
Nicholas I. M. Gould and
Wil H. A. Schilders and
Andrew J. Wathen Implicit-Factorization Preconditioning
and Iterative Solvers for Regularized
Saddle-Point Systems . . . . . . . . . . 170--189
Robert Orsi Numerical Methods for Solving Inverse
Eigenvalue Problems for Nonnegative
Matrices . . . . . . . . . . . . . . . . 190--212
Steven Delvaux and
Marc Van Barel Structures preserved by matrix inversion 213--228
Steven Delvaux and
Marc Van Barel Structures Preserved by Schur
Complementation . . . . . . . . . . . . 229--252
Damien Lemonnier and
Paul Van Dooren Balancing Regular Matrix Pencils . . . . 253--263
Christopher C. Paige and
Miroslav Rozlozník and
Zdenvek Strakos Modified Gram--Schmidt (MGS), Least
Squares, and Backward Stability of
MGS-GMRES . . . . . . . . . . . . . . . 264--284
Robert Granat and
Bo Kågström Direct Eigenvalue Reordering in a
Product of Matrices in Periodic Schur
Form . . . . . . . . . . . . . . . . . . 285--300
Chi-Kwong Li and
Roy Mathias Distances from a Hermitian Pair to
Diagonalizable and Nondiagonalizable
Hermitian Pairs . . . . . . . . . . . . 301--305
Luca Benvenuti and
Lorenzo Farina The Geometry of the Reachability Set for
Linear Discrete-time Systems with
Positive Controls . . . . . . . . . . . 306--325
Ralph Byers and
Daniel Kressner Structured Condition Numbers for
Invariant Subspaces . . . . . . . . . . 326--347
Ming Gu and
Michael L. Overton An Algorithm to Compute \boldmath $ {\rm
Sep}_\lambda $ . . . . . . . . . . . . . 348--359
Houduo Qi and
Defeng Sun A Quadratically Convergent Newton Method
for Computing the Nearest Correlation
Matrix . . . . . . . . . . . . . . . . . 360--385
Kolja Elssel and
Heinrich Voss An A Priori Bound for Automated
Multilevel Substructuring . . . . . . . 386--397
Dror Irony and
Sivan Toledo The Snap-Back Pivoting Method for
Symmetric Banded Indefinite Matrices . . 398--424
Amir Beck and
Aharon Ben-Tal and
Marc Teboulle Finding a Global Optimal Solution for a
Quadratically Constrained Fractional
Quadratic Problem with Applications to
the Regularized Total Least Squares . . 425--445
Arvind Sankar and
Daniel A. Spielman and
Shang-Hua Teng Smoothed Analysis of the Condition
Numbers and Growth Factors of Matrices 446--476
M. Gu and
E. Mengi and
M. L. Overton and
J. Xia and
J. Zhu Fast Methods for Estimating the Distance
to Uncontrollability . . . . . . . . . . 477--502
Bruno Iannazzo On the Newton Method for the Matrix $P$
th Root . . . . . . . . . . . . . . . . 503--523
Na Li and
Yousef Saad MIQR: a Multilevel Incomplete $ Q R $
Preconditioner for Large Sparse
Least-Squares Problems . . . . . . . . . 524--550
Claude Brezinski and
Michela Redivo-Zaglia The PageRank Vector: Properties,
Computation, Approximation, and
Acceleration . . . . . . . . . . . . . . 551--575
Haw-ren Fang and
Dianne P. O'Leary Stable Factorizations of Symmetric
Tridiagonal and Triadic Matrices . . . . 576--595
Harald K. Wimmer Inertial Signatures of Hermitian
Polynomial Matrices . . . . . . . . . . 596--601
S. Chandrasekaran and
M. Gu and
T. Pals A Fast $ U L V $ Decomposition Solver
for Hierarchically Semiseparable
Representations . . . . . . . . . . . . 603--622
Roden J. A. David and
David S. Watkins Efficient Implementation of the
Multishift $ Q R $ Algorithm for the
Unitary Eigenvalue Problem . . . . . . . 623--633
Young-Ju Lee and
Jinbiao Wu and
Jinchao Xu and
Ludmil Zikatanov On the Convergence of Iterative Methods
for Semidefinite Linear Systems . . . . 634--641
Lieven De Lathauwer A Link between the Canonical
Decomposition in Multilinear Algebra and
Simultaneous Matrix Diagonalization . . 642--666
Hristo S. Sendov Generalized Hadamard Product and the
Derivatives of Spectral Functions . . . 667--681
Delin Chu and
Y. S. Hung A Matrix Pencil Approach to the Row by
Row Decoupling Problem for Descriptor
Systems . . . . . . . . . . . . . . . . 682--702
F. Wirth and
R. Stanojevi and
R. Shorten and
D. Leith Stochastic Equilibria of AIMD
Communication Networks . . . . . . . . . 703--723
G. Rodriguez Fast Solution of Toeplitz- and
Cauchy-Like Least-Squares Problems . . . 724--748
Mili I. Shah and
Danny C. Sorensen A Symmetry Preserving Singular Value
Decomposition . . . . . . . . . . . . . 749--769
Delin Chu and
Gene H. Golub On a Generalized Eigenvalue Problem for
Nonsquare Pencils . . . . . . . . . . . 770--787
Chun-Hua Guo and
Nicholas J. Higham A Schur--Newton Method for the Matrix
\boldmath $p$th Root and its Inverse . . 788--804
J. K. Reid and
J. A. Scott Reducing the Total Bandwidth of a Sparse
Unsymmetric Matrix . . . . . . . . . . . 805--821
Driss Drissi Sharp Inequalities for Some Operator
Means . . . . . . . . . . . . . . . . . 822--828
Ren-Cang Li Asymptotically Optimal Lower Bounds for
the Condition Number of a Real
Vandermonde Matrix . . . . . . . . . . . 829--844
Yousef Saad Filtered Conjugate Residual-type
Algorithms with Applications . . . . . . 845--870
Sabine Le Borne Multilevel Hierarchical Matrices . . . . 871--889
Yongge Tian and
Yonghui Liu Extremal Ranks of Some Symmetric Matrix
Expressions with Applications . . . . . 890--905
Paul R. Willems and
Bruno Lang and
Christof Vömel Computing the Bidiagonal SVD Using
Multiple Relatively Robust
Representations . . . . . . . . . . . . 907--926
U. L. Hetmaniuk and
R. B. Lehoucq Uniform accuracy of eigenpairs from a
shift-invert Lanczos method . . . . . . 927--948
Ninoslav Truhar Relative Residual Bounds for Eigenvalues
of Hermitian Matrices . . . . . . . . . 949--960
Alexander N. Malyshev Computation of Smallest Eigenvalues in
the Sturm--Liouville Problem with
Strongly Varying Coefficients . . . . . 961--970
D. Steven Mackey and
Niloufer Mackey and
Christian Mehl and
Volker Mehrmann Vector Spaces of Linearizations for
Matrix Polynomials . . . . . . . . . . . 971--1004
Nicholas J. Higham and
D. Steven Mackey and
Françoise Tisseur The Conditioning of Linearizations of
Matrix Polynomials . . . . . . . . . . . 1005--1028
D. Steven Mackey and
Niloufer Mackey and
Christian Mehl and
Volker Mehrmann Structured Polynomial Eigenvalue
Problems: Good Vibrations from Good
Linearizations . . . . . . . . . . . . . 1029--1051
Michael Karow and
Daniel Kressner and
Françoise Tisseur Structured Eigenvalue Condition Numbers 1052--1068
Jörg Berns-Müller and
Alastair Spence Inexact Inverse Iteration with Variable
Shift for Nonsymmetric Generalized
Eigenvalue Problems . . . . . . . . . . 1069--1082
S. K. Godunov and
M. Sadkane Spectral Analysis of Symplectic Matrices
with Application to the Theory of
Parametric Resonance . . . . . . . . . . 1083--1096
Luka Grubi'i On Eigenvalue and Eigenvector Estimates
for Nonnegative Definite Operators . . . 1097--1125
Froilán M. Dopico and
Plamen Koev Accurate Symmetric Rank Revealing and
Eigendecompositions of Symmetric
Structured Matrices . . . . . . . . . . 1126--1156
Bor Plestenjak Numerical Methods for the Tridiagonal
Hyperbolic Quadratic Eigenvalue Problem 1157--1172
María José Peláez and
Julio Moro Accurate Factorization and Eigenvalue
Algorithms for Symmetric DSTU and TSC
Matrices . . . . . . . . . . . . . . . . 1173--1198
Ilse C. F. Ipsen Special Issue on Accurate Solution Of
Eigenvalue Problems . . . . . . . . . . ix--ix
Per Christian Hansen and
Toke Koldborg Jensen Smoothing-Norm Preconditioning for
Regularizing Minimum-Residual Methods 1--14
Andrew V. Knyazev and
Merico E. Argentati Majorization for Changes in Angles
Between Subspaces, Ritz Values, and
Graph Laplacian Spectra . . . . . . . . 15--32
Yuen-Cheng Kuo and
Wen-Wei Lin and
Shu-Fang Xu Solutions of the Partially Described
Inverse Quadratic Eigenvalue Problem . . 33--53
Yongdo Lim The Matrix Golden Mean and Its
Applications to Riccati Matrix Equations 54--66
S. Chandrasekaran and
P. Dewilde and
M. Gu and
W. Lyons and
T. Pals A Fast Solver for HSS Representations
via Sparse Matrices . . . . . . . . . . 67--81
Chen Greif and
James M. Varah Minimizing the Condition Number for
Small Rank Modifications . . . . . . . . 82--97
Reinhard Nabben and
Daniel B. Szyld Schwarz Iterations for Symmetric
Positive Semidefinite Problems . . . . . 98--116
Holger Dette and
Bettina Reuther and
W. J. Studden and
M. Zygmunt Matrix Measures and Random Walks with a
Block Tridiagonal Transition Matrix . . 117--142
Nicholas J. Higham and
D. Steven Mackey and
Niloufer Mackey and
Françoise Tisseur Symmetric Linearizations for Matrix
Polynomials . . . . . . . . . . . . . . 143--159
M. Alanelli and
A. Hadjidimos A New Iterative Criterion for
$H$-Matrices . . . . . . . . . . . . . . 160--176
Carla D. Moravitz Martin and
Charles F. Van Loan Solving Real Linear Systems with the
Complex Schur Decomposition . . . . . . 177--183
Carla D. Moravitz Martin and
Charles F. Van Loan Shifted Kronecker Product Systems . . . 184--198
Bo Kågström and
Daniel Kressner Multishift Variants of the QZ Algorithm
with Aggressive Early Deflation . . . . 199--227
Patrick R. Amestoy and
Xiaoye S. Li and
Esmond G. Ng Diagonal Markowitz Scheme with Local
Symmetrization . . . . . . . . . . . . . 228--244
Satoru Iwata and
Ryo Shimizu Combinatorial Analysis of Singular
Matrix Pencils . . . . . . . . . . . . . 245--259
Daniele Bertaccini and
Gene H. Golub and
Stefano Serra-Capizzano Spectral Analysis of a Preconditioned
Iterative Method for the
Convection-Diffusion Equation . . . . . 260--278
Peter Lancaster Inverse Spectral Problems for Semisimple
Damped Vibrating Systems . . . . . . . . 279--301
Patrick R. Amestoy and
Xiaoye S. Li and
Stéphane Pralet Unsymmetric Ordering Using a Constrained
Markowitz Scheme . . . . . . . . . . . . 302--327
Vincent Arsigny and
Pierre Fillard and
Xavier Pennec and
Nicholas Ayache Geometric Means in a Novel Vector Space
Structure on Symmetric Positive-Definite
Matrices . . . . . . . . . . . . . . . . 328--347
Vjeran Hari Convergence of a Block-Oriented
Quasi-Cyclic Jacobi Method . . . . . . . 349--369
Charles R. Johnson and
Ronald L. Smith Path Product Matrices and Eventually
Inverse $M$-matrices . . . . . . . . . . 370--376
Hüseyin Akçay and
Semiha Türkay A Subspace-Based Method for Solving
Lagrange--Sylvester Interpolation
Problems . . . . . . . . . . . . . . . . 377--395
Chun-Hua Guo and
Nicholas J. Higham Iterative Solution of a Nonsymmetric
Algebraic Riccati Equation . . . . . . . 396--412
Mario Arioli and
Marc Baboulin and
Serge Gratton A Partial Condition Number for Linear
Least Squares Problems . . . . . . . . . 413--433
Othmar Koch and
Christian Lubich Dynamical Low-Rank Approximation . . . . 434--454
I. Baragaña and
V. Fernández and
I. Zaballa Hermite Indices and Jordan Structure of
a Perturbed Linear System . . . . . . . 455--472
Z. D. Bai and
L. X. Zhang Semicircle Law for Hadamard Products . . 473--495
Fernando De Terán and
Froilán M. Dopico Low Rank Perturbation of Kronecker
Structures without Full Rank . . . . . . 496--529
Zhenyue Zhang and
Min Fang and
Jing Wang Stability and Fast Algorithms of
Incomplete $ L U $ Factorization with
Zero-Fill for Nine-Diagonal Matrices . . 530--553
In-Jae Kim and
D. D. Olesky and
B. L. Shader and
P. van den Driessche Sign Patterns That Allow a Positive or
Nonnegative Left Inverse . . . . . . . . 554--565
D. A. Bini and
Y. Eidelman and
L. Gemignani and
I. Gohberg Fast $ Q R $ Eigenvalue Algorithms for
Hessenberg Matrices Which Are Rank-One
Perturbations of Unitary Matrices . . . 566--585
J. V. Burke and
A. S. Lewis and
M. L. Overton Convexity and Lipschitz Behavior of
Small Pseudospectra . . . . . . . . . . 586--595
Erik G. Boman and
Stephen Guattery and
Bruce Hendrickson Optimal Embeddings and Eigenvalues in
Support Theory . . . . . . . . . . . . . 596--605
Amir Beck and
Yonina C. Eldar Regularization in Regression with
Bounded Noise: a Chebyshev Center
Approach . . . . . . . . . . . . . . . . 606--625
Hans Georg Bock and
Ekaterina Kostina and
Olga Kostyukova Covariance Matrices for Parameter
Estimates of Constrained Parameter
Estimation Problems . . . . . . . . . . 626--642
Wen Li and
Weiwei Sun Combined Perturbation Bounds: I.
Eigensystems and Singular Value
Decompositions . . . . . . . . . . . . . 643--655
Shmuel Friedland and
Anatoli Torokhti Generalized Rank-Constrained Matrix
Approximations . . . . . . . . . . . . . 656--659
Albrecht Böttcher and
Jani Virtanen Norms of Toeplitz Matrices with
Fisher--Hartwig Symbols . . . . . . . . 660--671
H. S. Dollar Constraint-Style Preconditioners for
Regularized Saddle Point Problems . . . 672--684
Sergio Albeverio and
Alexander K. Motovilov and
Alexei V. Selin The a Priori $ \tan \Theta $ Theorem for
Eigenvectors . . . . . . . . . . . . . . 685--697
Thomas Ransford On Pseudospectra and Power Growth . . . 699--711
Amir Beck and
Yonina C. Eldar and
Aharon Ben-Tal Mean-Squared Error Estimation for Linear
Systems with Block Circulant Uncertainty 712--730
Plamen Koev Accurate Computations with Totally
Nonnegative Matrices . . . . . . . . . . 731--751
Joachim Schöberl and
Walter Zulehner Symmetric Indefinite Preconditioners for
Saddle Point Problems with Applications
to PDE-Constrained Optimization Problems 752--773
Gene H. Golub and
Daniel Ruiz and
Ahmed Touhami A Hybrid Approach Combining Chebyshev
Filter and Conjugate Gradient for
Solving Linear Systems with Multiple
Right-Hand Sides . . . . . . . . . . . . 774--795
Jeffrey S. Geronimo and
Hugo Woerdeman Two Variable Orthogonal Polynomials on
the BiCircle and Structured Matrices . . 796--825
Carlos Campos and
David Guerrero and
Vicente Hernández and
Rui Ralha Parallel Bidiagonalization of a Dense
Matrix . . . . . . . . . . . . . . . . . 826--837
Hua Xiang and
Yimin Wei On Normwise Structured Backward Errors
for Saddle Point Systems . . . . . . . . 838--849
Seak-Weng Vong and
Xiao-Qing Jin Unitarily Invariant Norms of Toeplitz
Matrices with Fisher--Hartwig
Singularities . . . . . . . . . . . . . 850--854
Daniel R. Fuhrmann Numerically Stable Implementations of
the Structured Covariance
Expectation-Maximization Algorithm . . . 855--869
Lars Grasedyck and
Wolfgang Hackbusch A Multigrid Method to Solve Large Scale
Sylvester Equations . . . . . . . . . . 870--894
Steven Delvaux and
Marc Van Barel A Hessenberg Reduction Algorithm for
Rank Structured Matrices . . . . . . . . 895--926
Nela Bosner and
Jesse L. Barlow Block and Parallel Versions of One-Sided
Bidiagonalization . . . . . . . . . . . 927--953
Yunkai Zhou and
Yousef Saad A Chebyshev--Davidson Algorithm for
Large Symmetric Eigenproblems . . . . . 954--971
Shuangquan Wang and
Ali Abdi Joint Singular Value Distribution of Two
Correlated Rectangular Gaussian Matrices
and Its Application . . . . . . . . . . 972--981
Eric King-Wah Chu and
Hung-Yuan Fan and
Wen-Wei Lin Projected Generalized Discrete-Time
Periodic Lyapunov Equations and Balanced
Realization of Periodic Descriptor
Systems . . . . . . . . . . . . . . . . 982--1006
Iain S. Duff and
Stéphane Pralet Towards Stable Mixed Pivoting Strategies
for the Sequential and Parallel Solution
of Sparse Symmetric Indefinite Systems 1007--1024
Peter Buchholz and
Tu rul Dayar On the Convergence of a Class of
Multilevel Methods for Large Sparse
Markov Chains . . . . . . . . . . . . . 1025--1049
E. B. Davies Approximate Diagonalization . . . . . . 1051--1064
Damon Hyde and
Misha Kilmer and
Dana H. Brooks and
Eric Miller Analysis and Exploitation of Matrix
Structure Arising in Linearized Optical
Tomographic Imaging . . . . . . . . . . 1065--1082
Chun-Hua Guo and
Bruno Iannazzo and
Beatrice Meini On the Doubling Algorithm for a
(Shifted) Nonsymmetric Algebraic Riccati
Equation . . . . . . . . . . . . . . . . 1083--1100
Wai-Ki Ching and
Michael K. Ng and
You-Wei Wen Block Diagonal and Schur Complement
Preconditioners for Block-Toeplitz
Systems with Small Size Blocks . . . . . 1101--1119
Inderjit S. Dhillon and
Joel A. Tropp Matrix Nearness Problems with Bregman
Divergences . . . . . . . . . . . . . . 1120--1146
Steven Delvaux and
Marc Van Barel A Givens-Weight Representation for Rank
Structured Matrices . . . . . . . . . . 1147--1170
Jörg Liesen When is the Adjoint of a Matrix a Low
Degree Rational Function in the Matrix? 1171--1180
André C. M. Ran and
Leiba Rodman On the Index of Conditional Stability of
Stable Invariant Lagrangian Subspaces 1181--1190
André Klein and
Peter Spreij Recursive Solution of Certain Structured
Linear Systems . . . . . . . . . . . . . 1191--1217
Nicholas J. Higham and
Ren-Cang Li and
Françoise Tisseur Backward Error of Polynomial
Eigenproblems Solved by Linearization 1218--1241
Dragan S. Djordjevi\'c Further Results on the Reverse Order Law
for Generalized Inverses . . . . . . . . 1242--1246
S. Chandrasekaran and
M. Gu and
X. Sun and
J. Xia and
J. Zhu A Superfast Algorithm for Toeplitz
Systems of Linear Equations . . . . . . 1247--1266
Andrew V. Knyazev and
Ilya Lashuk Steepest Descent and Conjugate Gradient
Methods with Variable Preconditioning 1267--1280
Ilse C. F. Ipsen and
Teresa M. Selee PageRank Computation, with Special
Attention to Dangling Nodes . . . . . . 1281--1296
Pavel Jiránek and
Miroslav Rozlo\vzník Maximum Attainable Accuracy of Inexact
Saddle Point Solvers . . . . . . . . . . 1297--1321
Zlatko Drma\vc and
Kre\vsimir Veseli\'c New Fast and Accurate Jacobi SVD
Algorithm. I . . . . . . . . . . . . . . 1322--1342
Zlatko Drma\vc and
Kre\vsimir Veseli\'c New Fast and Accurate Jacobi SVD
Algorithm. II . . . . . . . . . . . . . 1343--1362
Stanley C. Eisenstat and
Joseph W. H. Liu Algorithmic Aspects of Elimination Trees
for Sparse Unsymmetric Matrices . . . . 1363--1381
Zhi-Hao Cao On the Convergence of General Stationary
Linear Iterative Methods for Singular
Linear Systems . . . . . . . . . . . . . 1382--1388
D. Steven Mackey and
Niloufer Mackey and
Françoise Tisseur Structured Mapping Problems for Matrices
Associated with Scalar Products. Part I:
Lie and Jordan Algebras . . . . . . . . 1389--1410
Ioana Dumitriu and
Plamen Koev Distributions of the Extreme Eigenvalues
of Beta--Jacobi Random Matrices . . . . 1--6
Gil Shklarski and
Sivan Toledo Rigidity in Finite-Element Matrices:
Sufficient Conditions for the Rigidity
of Structures and Substructures . . . . 7--40
Pablo Lecumberri and
Marisol Gómez and
Alfonso Carlosena Generalized Eigenvalues of Nonsquare
Pencils with Structure . . . . . . . . . 41--55
Alexandre d'Aspremont and
Onureena Banerjee and
Laurent El Ghaoui First-Order Methods for Sparse
Covariance Selection . . . . . . . . . . 56--66
Johnathan M. Bardsley Wavefront Reconstruction Methods for
Adaptive Optics Systems on Ground-Based
Telescopes . . . . . . . . . . . . . . . 67--83
Gautam Bharali and
Olga Holtz Functions Preserving Nonnegativity of
Matrices . . . . . . . . . . . . . . . . 84--101
Bernhard Beckermann and
Lothar Reichel The Arnoldi Process and GMRES for Nearly
Symmetric Matrices . . . . . . . . . . . 102--120
Stijn Van Dongen Graph Clustering Via a Discrete
Uncoupling Process . . . . . . . . . . . 121--141
Wei Xu and
Sanzheng Qiao A Divide-and-Conquer Method for the
Takagi Factorization . . . . . . . . . . 142--153
Emre Mengi On the Estimation of the Distance to
Uncontrollability for Higher Order
Systems . . . . . . . . . . . . . . . . 154--172
Maurice Duits and
Arno B. J. Kuijlaars An Equilibrium Problem for the Limiting
Eigenvalue Distribution of Banded
Toeplitz Matrices . . . . . . . . . . . 173--196
Delin Chu and
Roger C. E. Tan Algebraic Characterizations for Positive
Realness of Descriptor Systems . . . . . 197--222
Csaba Mészáros On Numerical Issues of Interior Point
Methods . . . . . . . . . . . . . . . . 223--235
Achiya Dax Orthogonalization Via Deflation: a
Minimum Norm Approach for Low-Rank
Approximations of a Matrix . . . . . . . 236--260
Philip A. Knight The Sinkhorn--Knopp Algorithm:
Convergence and Applications . . . . . . 261--275
Dario A. Bini and
Bruno Iannazzo and
Federico Poloni A Fast Newton's Method for a
Nonsymmetric Algebraic Riccati Equation 276--290
Christian Mehl On Asymptotic Convergence of
Nonsymmetric Jacobi Algorithms . . . . . 291--311
N. D. Atreas and
C. Karanikas and
P. Polychronidou A Class of Sparse Unimodular Matrices
Generating Multiresolution and Sampling
Analysis for Data of Any Length . . . . 312--323
Catherine Fraikin and
Yurii Nesterov and
Paul Van Dooren Optimizing the Coupling Between Two
Isometric Projections of Matrices . . . 324--345
Joost Rommes and
Gerard L. G. Sleijpen Convergence of the Dominant Pole
Algorithm and Rayleigh Quotient
Iteration . . . . . . . . . . . . . . . 346--363
Gang Wu and
Yimin Wei Comments on: ``Jordan canonical form of
the Google matrix: a potential
contribution to the PageRank
computation'' [SIAM J. Matrix Anal.
Appl. \bf 27 (2005), no. 2, 305--312;
MR2179674] by S. Serra-Capizzano . . . . 364--374
Justin Brickell and
Inderjit S. Dhillon and
Suvrit Sra and
Joel A. Tropp The Metric Nearness Problem . . . . . . 375--396
C. Bekas and
E. Kokiopoulou and
Yousef Saad Computation of Large Invariant Subspaces
Using Polynomial Filtered Lanczos
Iterations with Applications in Density
Functional Theory . . . . . . . . . . . 397--418
Amir Beck and
Aharon Ben-Tal and
Christian Kanzow A Fast Method for Finding the Global
Solution of the Regularized Structured
Total Least Squares Problem for Image
Deblurring . . . . . . . . . . . . . . . 419--443
Craig Gotsman and
Sivan Toledo On the Computation of Null Spaces of
Sparse Rectangular Matrices . . . . . . 445--463
Steven Delvaux and
Marc Van Barel A $ Q R $-Based Solver for Rank
Structured Matrices . . . . . . . . . . 464--490
Fernando De Terán and
Froilán M. Dopico A Note on Generic Kronecker Orbits of
Matrix Pencils with Fixed Rank . . . . . 491--496
Mohamed A. El-Shehawey On Inverses of Tridiagonal Matrices
Arising From Markov Chain-Random Walk I 497--508
Milan Hladík Description of Symmetric and
Skew--Symmetric Solution Set . . . . . . 509--521
Kensuke Aishima and
Takayasu Matsuo and
Kazuo Murota and
Masaaki Sugihara On Convergence of the DQDS Algorithm for
Singular Value Computation . . . . . . . 522--537
Fernando de Terán and
Froilán M. Dopico and
Julio Moro Low Rank Perturbation of Weierstrass
Structure . . . . . . . . . . . . . . . 538--547
M. E. Argentati and
A. V. Knyazev and
C. C. Paige and
I. Panayotov Bounds on Changes in Ritz Values for a
Perturbed Invariant Subspace of a
Hermitian Matrix . . . . . . . . . . . . 548--559
Chi-Kwong Li and
Yiu-Tung Poon and
Nung-Sing Sze Eigenvalues of the Sum of Matrices from
Unitary Similarity Orbits . . . . . . . 560--581
Martin Stoll and
Andy Wathen Combination Preconditioning and the
Bramble--Pasciak Preconditioner . . . . 582--608
S. Gugercin and
A. C. Antoulas and
C. Beattie $ \mathcal {H}_2 $ Model Reduction for
Large-Scale Linear Dynamical Systems . . 609--638
Allan R. Willms Analytic Results for the Eigenvalues of
Certain Tridiagonal Matrices . . . . . . 639--656
M. Popolizio and
V. Simoncini Acceleration Techniques for
Approximating the Matrix Exponential
Operator . . . . . . . . . . . . . . . . 657--683
Yogi A. Erlangga and
Reinhard Nabben Deflation and Balancing Preconditioners
for Krylov Subspace Methods Applied to
Nonsymmetric Matrices . . . . . . . . . 684--699
Dimitrios Noutsos and
Michael J. Tsatsomeros Reachability and Holdability of
Nonnegative States . . . . . . . . . . . 700--712
Hyunsoo Kim and
Haesun Park Nonnegative Matrix Factorization Based
on Alternating Nonnegativity Constrained
Least Squares and Active Set Method . . 713--730
Matthew Booth and
Philip Hackney and
Benjamin Harris and
Charles R. Johnson and
Margaret Lay and
Lon H. Mitchell and
Sivaram K. Narayan and
Amanda Pascoe and
Kelly Steinmetz and
Brian D. Sutton and
Wendy Wang On the Minimum Rank Among Positive
Semidefinite Matrices with a Given Graph 731--740
F. Alberto Grünbaum and
Manuel D. de la Iglesia Matrix Valued Orthogonal Polynomials
Arising from Group Representation Theory
and a Family of Quasi-Birth-and-Death
Processes . . . . . . . . . . . . . . . 741--761
Ilse C. F. Ipsen and
Rizwana Rehman Perturbation Bounds for Determinants and
Characteristic Polynomials . . . . . . . 762--776
Rafael Cantó and
Plamen Koev and
Beatriz Ricarte and
Ana M. Urbano $ L D U $ Factorization of Nonsingular
Totally Nonpositive Matrices . . . . . . 777--782
William W. Hager and
Jiangtao Luo Optimization of Generalized Mean-Square
Error in Noisy Linear Estimation . . . . 783--804
Daniel Kressner The Effect of Aggressive Early Deflation
on the Convergence of the $ Q R $
Algorithm . . . . . . . . . . . . . . . 805--821
Ralph Byers and
Hongguo Xu A New Scaling for Newton's Iteration for
the Polar Decomposition and its Backward
Stability . . . . . . . . . . . . . . . 822--843
Petros Drineas and
Michael W. Mahoney and
S. Muthukrishnan Relative-Error $ C U R $ Matrix
Decompositions . . . . . . . . . . . . . 844--881
N. Castro-González and
J. Robles and
J. Y. Vélez-Cerrada Characterizations of a Class of Matrices
and Perturbation of the Drazin Inverse 882--897
Hu Yang and
Hanyu Li Weighted Polar Decomposition and WGL
Partial Ordering of Rectangular Complex
Matrices . . . . . . . . . . . . . . . . 898--924
Andreas Frommer and
Reinhard Nabben and
Daniel B. Szyld Convergence of Stationary Iterative
Methods for Hermitian Semidefinite
Linear Systems and Applications to
Schwarz Methods . . . . . . . . . . . . 925--938
I. V. Oseledets and
D. V. Savostianov and
E. E. Tyrtyshnikov Tucker Dimensionality Reduction of
Three-Dimensional Arrays in Linear Time 939--956
Michael W. Mahoney and
Mauro Maggioni and
Petros Drineas Tensor-CUR Decompositions for
Tensor-Based Data . . . . . . . . . . . 957--987
Alwin Stegeman Low-Rank Approximation of Generic $ p
\times q \times 2 $ Arrays and Diverging
Components in the Candecomp/Parafac
Model . . . . . . . . . . . . . . . . . 988--1007
Roland Badeau and
Rémy Boyer Fast Multilinear Singular Value
Decomposition for Structured Tensors . . 1008--1021
Lieven De Lathauwer Decompositions of a Higher-Order Tensor
in Block Terms---Part I: Lemmas for
Partitioned Matrices . . . . . . . . . . 1022--1032
Lieven De Lathauwer Decompositions of a Higher-Order Tensor
in Block Terms---Part II: Definitions
and Uniqueness . . . . . . . . . . . . . 1033--1066
Lieven De Lathauwer and
Dimitri Nion Decompositions of a Higher-Order Tensor
in Block Terms---Part III: Alternating
Least Squares Algorithms . . . . . . . . 1067--1083
Vin de Silva and
Lek-Heng Lim Tensor Rank and the Ill-Posedness of the
Best Low-Rank Approximation Problem . . 1084--1127
Myriam Rajih and
Pierre Comon and
Richard A. Harshman Enhanced Line Search: a Novel Method to
Accelerate PARAFAC . . . . . . . . . . . 1128--1147
Bijan Afsari Sensitivity Analysis for the Problem of
Matrix Joint Diagonalization . . . . . . 1148--1171
Damien Muti and
Salah Bourennane and
Julien Marot Lower-Rank Tensor Approximation and
Multiway Filtering . . . . . . . . . . . 1172--1204
Marcel Joho Newton Method for Joint Approximate
Diagonalization of Positive Definite
Hermitian Matrices . . . . . . . . . . . 1205--1218
Carla D. Moravitz Martin and
Charles F. Van Loan A Jacobi-Type Method for Computing
Orthogonal Tensor Decompositions . . . . 1219--1232
Wolfgang Hackbusch and
Boris N. Khoromskij Tensor-Product Approximation to
Multidimensional Integral Operators and
Green's Functions . . . . . . . . . . . 1233--1253
Pierre Comon and
Gene Golub and
Lek-Heng Lim and
Bernard Mourrain Symmetric Tensors and Symmetric Tensor
Rank . . . . . . . . . . . . . . . . . . 1254--1279
Lieven De Lathauwer and
Pierre Comon and
Nicola Mastronardi Special Issue on Tensor Decompositions
and Applications . . . . . . . . . . . . vii--vii
X.-W. Chang and
G. H. Golub and
C. C. Paige Towards a Backward Perturbation Analysis
For Data Least Squares Problems . . . . 1281--1301
Natacha Béreux Out-of-Core Implementations of Cholesky
Factorization: Loop-Based versus
Recursive Algorithms . . . . . . . . . . 1302--1319
T. Betcke Optimal Scaling of Generalized and
Polynomial Eigenvalue Problems . . . . . 1320--1338
Volker Mehrmann and
Hongguo Xu Explicit Solutions for a Riccati
Equation from Transport Theory . . . . . 1339--1357
Xiao-Shan Chen and
Wen Li A Note on Backward Error Analysis of the
Generalized Singular Value Decomposition 1358--1370
Stefan Borovac A Graph Based Approach to the
Convergence of One Level Schwarz
Iterations for Singular $M$-Matrices and
Markov Chains . . . . . . . . . . . . . 1371--1391
G. Alefeld and
G. Mayer New Criteria for the Feasibility of the
Cholesky Method with Interval Data . . . 1392--1405
X.-W. Chang and
C. C. Paige and
D. Titley-Peloquin Characterizing Matrices That Are
Consistent with Given Solutions . . . . 1406--1420
Zhi-Hao Cao A Note on Eigenvalues of Matrices Which
Are Self-Adjoint in Symmetric Bilinear
Forms . . . . . . . . . . . . . . . . . 1421--1423
Pinar Heggernes and
Barry W. Peyton Fast Computation of Minimal Fill Inside
a Given Elimination Ordering . . . . . . 1424--1444
Bruno Iannazzo A Family of Rational Iterations and Its
Application to the Computation of the
Matrix $p$ th Root . . . . . . . . . . . 1445--1462
Karl Meerbergen The Quadratic Arnoldi Method for the
Solution of the Quadratic Eigenvalue
Problem . . . . . . . . . . . . . . . . 1463--1482
Pavel Jiránek and
Miroslav Rozlo\vzník and
Martin H. Gutknecht How to Make Simpler GMRES and GCR More
Stable . . . . . . . . . . . . . . . . . 1483--1499
Carl Christian Kjelgaard Mikkelsen and
Murat Manguoglu Analysis of the Truncated SPIKE
Algorithm . . . . . . . . . . . . . . . 1500--1519
Laura Grigori and
John R. Gilbert and
Michel Cosnard Symbolic and Exact Structure Prediction
for Sparse Gaussian Elimination with
Partial Pivoting . . . . . . . . . . . . 1520--1545
Fasma Diele and
Igor Moret and
Stefania Ragni Error Estimates for Polynomial Krylov
Approximations to Matrix Functions . . . 1546--1565
Tsung-Ming Huang and
Wen-Wei Lin and
Jiang Qian Structure-Preserving Algorithms for
Palindromic Quadratic Eigenvalue
Problems Arising from Vibration of Fast
Trains . . . . . . . . . . . . . . . . . 1566--1592
Chun-Hua Guo and
Nicholas J. Higham and
Françoise Tisseur Detecting and Solving Hyperbolic
Quadratic Eigenvalue Problems . . . . . 1593--1613
Alwin Stegeman and
Lieven De Lathauwer A Method to Avoid Diverging Components
in the Candecomp/Parafac Model for
Generic $ I \times J \times 2 $ Arrays 1614--1638
Awad H. Al-Mohy and
Nicholas J. Higham Computing the Fréchet Derivative of the
Matrix Exponential, with an Application
to Condition Number Estimation . . . . . 1639--1657
A. J. Laub and
J. Xia Fast Condition Estimation for a Class of
Structured Eigenvalue Problems . . . . . 1658--1676
Rebecca S. Wills and
Ilse C. F. Ipsen Ordinal Ranking for Google's PageRank 1677--1696
Takuma Kimura and
Xiaojun Chen Validated Solutions of Saddle Point
Linear Systems . . . . . . . . . . . . . 1697--1708
Jie Chen and
Yousef Saad On the Tensor SVD and the Optimal Low
Rank Orthogonal Approximation of Tensors 1709--1734
Delin Chu and
M. Malabre and
Roger C. E. Tan State Feedback Decoupling Problem with
Stability for $ (A, B, C, D) $
Quadruples . . . . . . . . . . . . . . . 1735--1760
Jürgen Garloff Interval Gaussian Elimination with Pivot
Tightening . . . . . . . . . . . . . . . 1761--1772
Chao Yang and
Weiguo Gao and
Juan C. Meza On the Convergence of the
Self-Consistent Field Iteration for a
Class of Nonlinear Eigenvalue Problems 1773--1788
Mark Embree The Arnoldi Eigenvalue Iteration with
Exact Shifts Can Fail . . . . . . . . . 1--10
Qiang Ye Relative Perturbation Bounds for
Eigenvalues of Symmetric Positive
Definite Diagonally Dominant Matrices 11--17
Ninoslav Truhar and
Kre\vsimir Veseli\'c An Efficient Method for Estimating the
Optimal Dampers' Viscosity for Linear
Vibrating Systems Using Lyapunov
Equation . . . . . . . . . . . . . . . . 18--39
I. C. F. Ipsen and
B. Nadler Refined Perturbation Bounds for
Eigenvalues of Hermitian and
Non-Hermitian Matrices . . . . . . . . . 40--53
Nela Bosner and
Zlatko Drma\vc Subspace Gap Residuals for
Rayleigh--Ritz Approximations . . . . . 54--67
Jason Slemons The Result of Two Steps of the $ L R $
Algorithm is Diagonally Similar to the
Result of One Step of the $ H R $
Algorithm . . . . . . . . . . . . . . . 68--74
Rui Ralha Perturbation Splitting for More Accurate
Eigenvalues . . . . . . . . . . . . . . 75--91
Mickaël Robbé and
Miloud Sadkane and
Alastair Spence Inexact Inverse Subspace Iteration with
Preconditioning Applied to Non-Hermitian
Eigenvalue Problems . . . . . . . . . . 92--113
Beresford N. Parlett and
Christof Vömel The Spectrum of a Glued Matrix . . . . . 114--132
J. Mateja\vs Accuracy of the Jacobi Method on Scaled
Diagonally Dominant Symmetric Matrices 133--153
Raf Vandebril and
Gene Golub and
Marc Van Barel A Quasi-Separable Approach to Solve the
Symmetric Definite Tridiagonal
Generalized Eigenvalue Problem . . . . . 154--174
Daniel Kressner and
María José Peláez and
Julio Moro Structured Hölder Condition Numbers for
Multiple Eigenvalues . . . . . . . . . . 175--201
Ilse C. F. Ipsen Special Issue on Accurate Solution of
Eigenvalue Problems . . . . . . . . . . vii--vii
Erik Elmroth and
Stefan Johansson and
Bo Kågström Stratification of Controllability and
Observability Pairs---Theory and Use in
Applications . . . . . . . . . . . . . . 203--226
Chun-Yueh Chiang and
Eric King-Wah Chu and
Chun-Hua Guo and
Tsung-Ming Huang and
Wen-Wei Lin and
Shu-Fang Xu Convergence Analysis of the Doubling
Algorithm for Several Nonlinear Matrix
Equations in the Critical Case . . . . . 227--247
Lars Eldén and
Berkant Savas A Newton--Grassmann Method for Computing
the Best Multilinear Rank-$ (r_1, r_2,
r_3) $ Approximation of a Tensor . . . . 248--271
F. Feitzinger and
T. Hylla and
E. W. Sachs Inexact Kleinman--Newton Method for
Riccati Equations . . . . . . . . . . . 272--288
Claude Dellacherie and
Servet Martinez and
Jaime San Martín Hadamard Functions of Inverse
$M$-Matrices . . . . . . . . . . . . . . 289--315
I. V. Oseledets and
D. V. Savostyanov and
E. E. Tyrtyshnikov Fast Simultaneous Orthogonal Reduction
to Triangular Matrices . . . . . . . . . 316--330
Bibhas Adhikari and
Rafikul Alam Structured Backward Errors and
Pseudospectra of Structured Matrix
Pencils . . . . . . . . . . . . . . . . 331--359
Michele Benzi A Generalization of the Hermitian and
Skew-Hermitian Splitting Iteration . . . 360--374
Luca Dieci and
Alessandro Pugliese Two-Parameter SVD: Coalescing Singular
Values and Periodicity . . . . . . . . . 375--403
R. M. Jungers and
V. Y. Protasov Counterexamples to the Complex Polytope
Extremality Conjecture . . . . . . . . . 404--409
Zhong-Zhi Bai and
Michael K. Ng and
Zeng-Qi Wang Constraint Preconditioners for Symmetric
Indefinite Matrices . . . . . . . . . . 410--433
Michael J. O'Sullivan and
Michael A. Saunders Stabilizing Policy Improvement for
Large-Scale Infinite-Horizon Dynamic
Programming . . . . . . . . . . . . . . 434--459
Michiel E. Hochstenbach and
Yvan Notay Controlling Inner Iterations in the
Jacobi--Davidson Method . . . . . . . . 460--477
Nicholas J. Higham and
D. Steven Mackey and
Françoise Tisseur Definite Matrix Polynomials and their
Linearization by Definite Pencils . . . 478--502
Tsung-Lin Lee and
Tien-Yien Li and
Zhonggang Zeng A Rank-Revealing Method with Updating,
Downdating, and Applications. Part II 503--525
Fabio Di Benedetto Gram Matrices of Fast Algebras Have a
Rank Structure . . . . . . . . . . . . . 526--545
Delin Chu and
Moody Chu and
Wen-Wei Lin Quadratic Model Updating with Symmetry,
Positive Definiteness, and No Spill-Over 546--564
Christopher C. Paige A Useful Form of Unitary Matrix Obtained
from Any Sequence of Unit $2$-Norm
$n$-Vectors . . . . . . . . . . . . . . 565--583
Chen Greif and
James M. Varah Iterative Solution of Skew-Symmetric
Linear Systems . . . . . . . . . . . . . 584--601
N. Guglielmi and
M. Zennaro Finding Extremal Complex Polytope Norms
for Families of Real Matrices . . . . . 602--620
Andrew V. Knyazev and
Klaus Neymeyr Gradient Flow Approach to Geometric
Convergence Analysis of Preconditioned
Eigensolvers . . . . . . . . . . . . . . 621--628
Thomas J. Laffey and
Raphael Loewy and
Helena \vSmigoc Nonnegative Matrices That Are Similar to
Positive Matrices . . . . . . . . . . . 629--649
Froilán M. Dopico and
Charles R. Johnson Parametrization of the Matrix Symplectic
Group and Applications . . . . . . . . . 650--673
Haim Avron and
Esmond Ng and
Sivan Toledo Using Perturbed $ Q R $ Factorizations
to Solve Linear Least-Squares Problems 674--693
Haim Avron and
Doron Chen and
Gil Shklarski and
Sivan Toledo Combinatorial Preconditioners for Scalar
Elliptic Finite-Element Problems . . . . 694--720
Dennis Cheung and
Felipe Cucker Componentwise Condition Numbers of
Random Sparse Matrices . . . . . . . . . 721--731
J. William Helton and
Igor Klep and
Raul Gomez Determinant Expansions of Signed
Matrices and of Certain Jacobians . . . 732--754
Jiawang Nie and
Bernd Sturmfels Matrix Cubes Parameterized by
Eigenvalues . . . . . . . . . . . . . . 755--766
Owe Axelsson and
Radim Blaheta and
Maya Neytcheva Preconditioning of Boundary Value
Problems Using Elementwise Schur
Complements . . . . . . . . . . . . . . 767--789
T. Bella and
Y. Eidelman and
I. Gohberg and
I. Koltracht and
V. Olshevsky A Fast Björck--Pereyra-Type Algorithm for
Solving
Hessenberg--Quasiseparable-Vandermonde
Systems . . . . . . . . . . . . . . . . 790--815
Shu-Qian Shen and
Ting-Zhu Huang and
Yan-Fei Jing On Inclusion and Exclusion Intervals for
the Real Eigenvalues of Real Matrices 816--830
X.-W. Chang and
C. C. Paige and
D. Titley-Peloquin Stopping Criteria for the Iterative
Solution of Linear Least Squares
Problems . . . . . . . . . . . . . . . . 831--852
Jörg Liesen and
Petr Tichý On Best Approximations of Polynomials in
Matrices in the Matrix $2$-Norm . . . . 853--863
Vincent D. Blondel and
Yurii Nesterov Polynomial-Time Computation of the Joint
Spectral Radius for Some Sets of
Nonnegative Matrices . . . . . . . . . . 865--876
Fei Xue and
Howard C. Elman Convergence Analysis of Iterative
Solvers in Inexact Rayleigh Quotient
Iteration . . . . . . . . . . . . . . . 877--899
Shreemayee Bora Structured Eigenvalue Condition Number
and Backward Error of a Class of
Polynomial Eigenvalue Problems . . . . . 900--917
Shuai Lu and
Sergei V. Pereverzev and
Ulrich Tautenhahn Regularized Total Least Squares:
Computational Aspects and Error Bounds 918--941
Melina A. Freitag and
Alastair Spence Shift-Invert Arnoldi's Method with
Preconditioned Iterative Solves . . . . 942--969
Awad H. Al-Mohy and
Nicholas J. Higham A New Scaling and Squaring Algorithm for
the Matrix Exponential . . . . . . . . . 970--989
Jorge Delgado and
J. M. Peña Optimal Conditioning of Bernstein
Collocation Matrices . . . . . . . . . . 990--996
Alessandro Russo and
Cristina Tablino Possio Preconditioned Hermitian and
Skew-Hermitian Splitting Method for
Finite Element Approximations of
Convection-Diffusion Equations . . . . . 997--1018
Mili I. Shah and
Danny C. Sorensen Best Nonspherical Symmetric Low Rank
Approximation . . . . . . . . . . . . . 1019--1039
Brian D. Ewald and
Jeffrey Humpherys and
Jeremy M. West Computing Expected Transition Events in
Reducible Markov Chains . . . . . . . . 1040--1054
Silv\`ere Bonnabel and
Rodolphe Sepulchre Riemannian Metric and Geometric Mean for
Positive Semidefinite Matrices of Fixed
Rank . . . . . . . . . . . . . . . . . . 1055--1070
Xiao-Wen Chang and
Gene H. Golub Solving Ellipsoid-Constrained Integer
Least Squares Problems . . . . . . . . . 1071--1089
Michael Ng and
Liqun Qi and
Guanglu Zhou Finding the Largest Eigenvalue of a
Nonnegative Tensor . . . . . . . . . . . 1090--1099
Vladimir Rokhlin and
Arthur Szlam and
Mark Tygert A Randomized Algorithm for Principal
Component Analysis . . . . . . . . . . . 1100--1124
William Anderson and
Martin T. Wells The Exact Distribution of the Condition
Number of a Gaussian Matrix . . . . . . 1125--1130
Chun-Hua Guo and
Nicholas J. Higham and
Françoise Tisseur An Improved Arc Algorithm for Detecting
Definite Hermitian Pairs . . . . . . . . 1131--1151
N. I. M. Gould and
V. Simoncini Spectral Analysis of Saddle Point
Matrices with Indefinite Leading Blocks 1152--1171
Tomonari Kitahara and
Takashi Tsuchiya Proximity of Weighted and Layered Least
Squares Solutions . . . . . . . . . . . 1172--1186
Delin Chu and
Y. S. Hung and
Hugo J. Woerdeman Inertia and Rank Characterizations of
Some Matrix Expressions . . . . . . . . 1187--1226
S. D. Eubanks and
J. J. McDonald On a Generalization of Soules Bases . . 1227--1234
Zhang Liu and
Lieven Vandenberghe Interior-Point Method for Nuclear Norm
Approximation with Application to System
Identification . . . . . . . . . . . . . 1235--1256
Marc Jungers and
Cristian Oar\ua and
Hisham Abou-Kandil and
Radu tefan General Matrix Pencil Techniques for
Solving Discrete-Time Nonsymmetric
Algebraic Riccati Equations . . . . . . 1257--1278
Andreas Frommer and
Behnam Hashemi Verified Computation of Square Roots of
a Matrix . . . . . . . . . . . . . . . . 1279--1302
Yves Nievergelt Why Lagrange Multipliers with Extreme
Magnitudes Give Extrema of Definite
Hermitian Forms on Quadric Surfaces . . 1303--1328
Zlatko Drma\vc A Global Convergence Proof for Cyclic
Jacobi Methods with Block Rotations . . 1329--1350
George Ostrouchov A Matrix Computation View of FastMap and
RobustMap Dimension Reduction Algorithms 1351--1360
Wolf Jürgen Beyn and
Vera Thümmler Continuation of Invariant Subspaces for
Parameterized Quadratic Eigenvalue
Problems . . . . . . . . . . . . . . . . 1361--1381
Jianlin Xia and
Shivkumar Chandrasekaran and
Ming Gu and
Xiaoye S. Li Superfast Multifrontal Method for Large
Structured Linear Systems of Equations 1382--1411
P. Butkovi\vc and
R. A. Cuninghame-Green and
S. Gaubert Reducible Spectral Theory with
Applications to the Robustness of
Matrices in Max-Algebra . . . . . . . . 1412--1431
Yan Gao and
Defeng Sun Calibrating Least Squares Semidefinite
Programming with Equality and Inequality
Constraints . . . . . . . . . . . . . . 1432--1457
G. W. Stewart On the Semidefinite $B$-Arnoldi Method 1458--1468
Alwin Stegeman and
André L. F. de Almeida Uniqueness Conditions for Constrained
Three-Way Factor Decompositions with
Linearly Dependent Loadings . . . . . . 1469--1490
Carlos Beltrán and
Jean-Pierre Dedieu and
Gregorio Malajovich and
Mike Shub Convexity Properties of the Condition
Number . . . . . . . . . . . . . . . . . 1491--1506
Qingxiang Xu and
Chuanning Song and
Yimin Wei The Stable Perturbation of the Drazin
Inverse of the Square Matrices . . . . . 1507--1520
Andrew V. Knyazev and
Merico E. Argentati Rayleigh--Ritz Majorization Error Bounds
with Applications to FEM . . . . . . . . 1521--1537
Andrzej Kie\lbasi\'nski and
Krystyna Zi\ketak Note on ``A New Scaling for Newton's
Iteration for the Polar Decomposition
and Its Backward Stability'' by R. Byers
and H. Xu . . . . . . . . . . . . . . . 1538--1539
Vartan Choulakian Some Numerical Results on the Rank of
Generic Three-Way Arrays over $ \mathbb
{R} $ . . . . . . . . . . . . . . . . . 1541--1551
Sandrine Bargiacchi-Soula and
Jérôme Fehrenbach and
Mohamed Masmoudi From Linear to Nonlinear Large Scale
Systems . . . . . . . . . . . . . . . . 1552--1569
So Yeon Chun and
A. Shapiro Construction of Covariance Matrices with
a Specified Discrepancy Function
Minimizer, with Application to Factor
Analysis . . . . . . . . . . . . . . . . 1570--1583
Lei-Hong Zhang and
Li-Zhi Liao and
Michael K. Ng Fast Algorithms for the Generalized
Foley--Sammon Discriminant Analysis . . 1584--1605
Yanxia Zhang and
Li Qiu From Subadditive Inequalities of
Singular Values to Triangle Inequalities
of Canonical Angles . . . . . . . . . . 1606--1620
Amit Singer and
Mihai Cucuringu Uniqueness of Low-Rank Matrix Completion
by Rigidity Theory . . . . . . . . . . . 1621--1641
Karl Meerbergen and
Zhaojun Bai The Lanczos Method for Parameterized
Symmetric Linear Systems with Multiple
Right-Hand Sides . . . . . . . . . . . . 1642--1662
Eric Ngondiep and
Stefano Serra-Capizzano and
Debora Sesana Spectral Features and Asymptotic
Properties for $g$-Circulants and
$g$-Toeplitz Sequences . . . . . . . . . 1663--1687
Daniel Kressner and
Christine Tobler Krylov Subspace Methods for Linear
Systems with Tensor Product Structure 1688--1714
J. M. Tang and
S. P. MacLachlan and
R. Nabben and
C. Vuik A Comparison of Two-Level
Preconditioners Based on Multigrid and
Deflation . . . . . . . . . . . . . . . 1715--1739
Bernhard Beckermann and
Stefan Güttel and
Raf Vandebril On the Convergence of Rational Ritz
Values . . . . . . . . . . . . . . . . . 1740--1774
Erik S. Van Vleck On the Error in the Product $ Q R $
Decomposition . . . . . . . . . . . . . 1775--1791
Yun-Bin Zhao The Legendre--Fenchel Conjugate of the
Product of Two Positive Definite
Quadratic Forms . . . . . . . . . . . . 1792--1811
Cristobald de Kerchove and
Paul Van Dooren Iterative Filtering in Reputation
Systems . . . . . . . . . . . . . . . . 1812--1834
Kazufumi Ito and
Karl Kunisch and
Volker Schulz and
Ilia Gherman Approximate Nullspace Iterations for KKT
Systems . . . . . . . . . . . . . . . . 1835--1847
Oliver G. Ernst and
Elisabeth Ullmann Stochastic Galerkin Matrices . . . . . . 1848--1872
Qiang Zhang and
Richard T. Guy and
Robert J. Plemmons Matrix Structures and Parallel
Algorithms for Image Superresolution
Reconstruction . . . . . . . . . . . . . 1873--1893
Steven Delvaux and
Maurice Duits An Equilibrium Problem for the Limiting
Eigenvalue Distribution of Rational
Toeplitz Matrices . . . . . . . . . . . 1894--1914
Sk. Safique Ahmad and
Rafikul Alam and
Ralph Byers On Pseudospectra, Critical Points, and
Multiple Eigenvalues of Matrix Pencils 1915--1933
Junfeng Lu and
Zhenyue Zhang A Modified Nonlinear Inexact Uzawa
Algorithm with a Variable Relaxation
Parameter for the Stabilized Saddle
Point Problem . . . . . . . . . . . . . 1934--1957
Musheng Wei and
Xuehan Cheng and
Qian Wang A Canonical Decomposition of the Right
Invertible System with Applications . . 1958--1981
Karl Meerbergen and
Alastair Spence Inverse Iteration for Purely Imaginary
Eigenvalues with Application to the
Detection of Hopf Bifurcations in
Large-Scale Problems . . . . . . . . . . 1982--1999
Zhaosong Lu Adaptive First-Order Methods for General
Sparse Inverse Covariance Selection . . 2000--2016
Thomas J. Laffey and
Helena \vSmigoc Sufficient Conditions on Commutators for
a Pair of Stable Matrices to Have a
Common Solution to the Lyapunov Equation 2017--2028
Lars Grasedyck Hierarchical Singular Value
Decomposition of Tensors . . . . . . . . 2029--2054
Pavel Jiránek and
David Titley-Peloquin Estimating the Backward Error in LSQR 2055--2074
Ruth Curtain and
Leiba Rodman Analytic Solutions of Matrix Riccati
Equations with Analytic Coefficients . . 2075--2092
Wim Michiels and
Suat Gumussoy Characterization and Computation of $
\mathcal {H}_{\infty } $ Norms for
Time-Delay Systems . . . . . . . . . . . 2093--2115
Milan Hladík and
David Daney and
Elias Tsigaridas Bounds on Real Eigenvalues and Singular
Values of Interval Matrices . . . . . . 2116--2129
I. V. Oseledets Approximation of $ 2^d \times 2^d $
Matrices Using Tensor Decomposition . . 2130--2145
Vladimir Y. Protasov and
Raphaël M. Jungers and
Vincent D. Blondel Joint Spectral Characteristics of
Matrices: a Conic Programming Approach 2146--2162
Nicholas J. Higham and
Christian Mehl and
Françoise Tisseur The Canonical Generalized Polar
Decomposition . . . . . . . . . . . . . 2163--2180
Fernando De Terán and
Froilán M. Dopico and
D. Steven Mackey Fiedler Companion Linearizations and the
Recovery of Minimal Indices . . . . . . 2181--2204
Vance Faber and
Jörg Liesen and
Petr Tichý On Chebyshev Polynomials of Matrices . . 2205--2221
Yariv Ephraim and
Michael Tinston Iterative Schur Complement and
Multistage Wiener Filtering . . . . . . 2222--2238
Aubrey Clayton Quasi-Birth-and-Death Processes and
Matrix-Valued Orthogonal Polynomials . . 2239--2260
S. Chandrasekaran and
P. Dewilde and
M. Gu and
N. Somasunderam On the Numerical Rank of the
Off-Diagonal Blocks of Schur Complements
of Discretized Elliptic PDEs . . . . . . 2261--2290
Roland Herzog and
Ekkehard Sachs Preconditioned Conjugate Gradient Method
for Optimal Control Problems with
Control and State Constraints . . . . . 2291--2317
Marija Dodig and
Marko Sto\vsi\'c Combinatorics of Column Minimal Indices
and Matrix Pencil Completion Problems 2318--2346
Christopher C. Paige An Augmented Stability Result for the
Lanczos Hermitian Matrix
Tridiagonalization Process . . . . . . . 2347--2359
Othmar Koch and
Christian Lubich Dynamical Tensor Approximation . . . . . 2360--2375
Nicola Mastronardi and
Eugene E. Tyrtyshnikov and
Paul Van Dooren A Fast Algorithm for Updating and
Downsizing the Dominant Kernel Principal
Components . . . . . . . . . . . . . . . 2376--2399
Ken Hayami and
Jun-Feng Yin and
Tokushi Ito GMRES Methods for Least Squares Problems 2400--2430
Rafael Bru and
José Marín and
José Mas and
Miroslav T\ocircuma Improved Balanced Incomplete
Factorization . . . . . . . . . . . . . 2431--2452
Shu-Qian Shen and
Ting-Zhu Huang and
Juan Yu Eigenvalue Estimates for Preconditioned
Nonsymmetric Saddle Point Matrices . . . 2453--2476
Takeshi Ogita Accurate Matrix Factorization: Inverse $
L U $ and Inverse $ Q R $ Factorizations 2477--2497
Alwin Stegeman On Uniqueness of the $n$ th Order Tensor
Decomposition into Rank-1 Terms with
Linear Independence in One Mode . . . . 2498--2516
Yuning Yang and
Qingzhi Yang Further Results for Perron--Frobenius
Theorem for Nonnegative Tensors . . . . 2517--2530
P. Favati and
G. Lotti and
O. Menchi Stability of the Levinson Algorithm for
Toeplitz-Like Systems . . . . . . . . . 2531--2552
Bart Vandereycken and
Stefan Vandewalle A Riemannian Optimization Approach for
Computing Low-Rank Solutions of Lyapunov
Equations . . . . . . . . . . . . . . . 2553--2579
Paola Boito and
Jean-Pierre Dedieu The Condition Metric in the Space of
Rectangular Full Rank Matrices . . . . . 2580--2602
Rüdiger Borsdorf and
Nicholas J. Higham and
Marcos Raydan Computing a Nearest Correlation Matrix
with Factor Structure . . . . . . . . . 2603--2622
Amir Beck and
Yonina C. Eldar Structured Total Maximum Likelihood: An
Alternative to Structured Total Least
Squares . . . . . . . . . . . . . . . . 2623--2649
Ming Gu and
Xiaoye S. Li and
Panayot S. Vassilevski Direction-Preserving and Schur-Monotonic
Semiseparable Approximations of
Symmetric Positive Definite Matrices . . 2650--2664
Mathias Drton and
Josephine Yu On a Parametrization of Positive
Semidefinite Matrices with Zeros . . . . 2665--2680
Paul G. Constantine and
David F. Gleich and
Gianluca Iaccarino Spectral Methods for Parameterized
Matrix Equations . . . . . . . . . . . . 2681--2699
Yuji Nakatsukasa and
Zhaojun Bai and
François Gygi Optimizing Halley's Iteration for
Computing the Matrix Polar Decomposition 2700--2720
N. Mastronardi and
M. Ng and
E. E. Tyrtyshnikov Decay in Functions of Multiband Matrices 2721--2737
Paul Van Dooren and
Kyle A. Gallivan and
P.-A. Absil $ \mathcal {H}_2 $-Optimal Model
Reduction with Higher-Order Poles . . . 2738--2753
M. A. Olshanskii and
V. Simoncini Acquired Clustering Properties and
Solution of Certain Saddle Point Systems 2754--2768
Peter Bürgisser and
Felipe Cucker Smoothed Analysis of Moore--Penrose
Inversion . . . . . . . . . . . . . . . 2769--2783
Chun-Hua Guo and
Wen-Wei Lin Solving a Structured Quadratic
Eigenvalue Problem by a
Structure-Preserving Doubling Algorithm 2784--2801
Julien M. Hendrickx and
Alex Olshevsky Matrix $p$-Norms Are NP-Hard to
Approximate If $ p \neq 1, 2, \infty $ 2802--2812
Catherine E. Powell and
Elisabeth Ullmann Preconditioning Stochastic Galerkin
Saddle Point Systems . . . . . . . . . . 2813--2840
X.-W. Chang and
D. Stehlé Rigorous Perturbation Bounds of Some
Matrix Factorizations . . . . . . . . . 2841--2859
Michael Karow Structured Pseudospectra and the
Condition of a Nonderogatory Eigenvalue 2860--2881
Bubacarr Bah and
Jared Tanner Improved Bounds on Restricted Isometry
Constants for Gaussian Matrices . . . . 2882--2898
Jianlin Xia and
Ming Gu Robust Approximate Cholesky
Factorization of Rank-Structured
Symmetric Positive Definite Matrices . . 2899--2920
Lyonell Boulton and
Peter Lancaster Schur Decompositions of a Matrix and the
Boundary of Its Pseudospectrum . . . . . 2921--2933
Joseph F. Grcar Spectral Condition Numbers of Orthogonal
Projections and Full Rank Linear Least
Squares Residuals . . . . . . . . . . . 2934--2949
T. T. Ngo and
M. Bellalij and
Y. Saad The Trace Ratio Optimization Problem for
Dimensionality Reduction . . . . . . . . 2950--2971
Lei-Hong Zhang Riemannian Newton Method for the
Multivariate Eigenvalue Problem . . . . 2972--2996
Aaron Welters On Explicit Recursive Formulas in the
Spectral Perturbation Analysis of a
Jordan Block . . . . . . . . . . . . . . 1--22
Hwa-Long Gau and
Chi-Kwong Li and
Yiu-Tung Poon and
Nung-Sing Sze Higher Rank Numerical Ranges of Normal
Matrices . . . . . . . . . . . . . . . . 23--43
Satoru Iwata and
Mizuyo Takamatsu On the Kronecker Canonical Form of Mixed
Matrix Pencils . . . . . . . . . . . . . 44--71
Xinghua Shi and
Yimin Wei and
Wen Zhang Convergence of General Nonstationary
Iterative Methods for Solving Singular
Linear Equations . . . . . . . . . . . . 72--89
Rizwana Rehman and
Ilse C. F. Ipsen Computing Characteristic Polynomials
from Eigenvalues . . . . . . . . . . . . 90--114
Mariya Ishteva and
P.-A. Absil and
Sabine Van Huffel and
Lieven De Lathauwer Best Low Multilinear Rank Approximation
of Higher-Order Tensors, Based on the
Riemannian Trust-Region Scheme . . . . . 115--135
Bingsheng He and
Minghua Xu and
Xiaoming Yuan Solving Large-Scale Least Squares
Semidefinite Programming by Alternating
Direction Methods . . . . . . . . . . . 136--152
Ilse C. F. Ipsen and
Teresa M. Selee Ergodicity Coefficients Defined by
Vector Norms . . . . . . . . . . . . . . 153--200
Yangfeng Su and
Zhaojun Bai Solving Rational Eigenvalue Problems via
Linearization . . . . . . . . . . . . . 201--216
Raf Vandebril Chasing Bulges or Rotations? A
Metamorphosis of the $ Q R $-Algorithm 217--247
Beatrice Meini and
Federico Poloni A Perron Iteration for the Solution of a
Quadratic Vector Equation Arising in
Markovian Binary Trees . . . . . . . . . 248--261
Ferenc Domes and
Arnold Neumaier Rigorous Enclosures of Ellipsoids and
Directed Cholesky Factorizations . . . . 262--285
Paolo Bientinesi and
Robert A. van de Geijn Goal-Oriented and Modular Stability
Analysis . . . . . . . . . . . . . . . . 286--308
G. W. Stewart On the Numerical Analysis of Oblique
Projectors . . . . . . . . . . . . . . . 309--348
Yuri M. Nechepurenko and
Miloud Sadkane A Low-Rank Approximation for Computing
the Matrix Exponential Norm . . . . . . 349--363
Aliaksei Sandryhaila and
Jelena Kovacevi\'c and
Markus Püschel Algebraic Signal Processing Theory:
Cooley--Tukey-Type Algorithms for
Polynomial Transforms Based on Induction 364--384
Miklós Pálfia A Multivariable Extension of
Two-Variable Matrix Means . . . . . . . 385--393
Gérard Meurant On the Residual Norm in FOM and GMRES 394--411
Seak-weng Vong and
Zheng-jian Bai and
Xiao-qing Jin An Ulm-like Method for Inverse Singular
Value Problems . . . . . . . . . . . . . 412--429
Liqun Qi The Best Rank-One Approximation Ratio of
a Tensor Space . . . . . . . . . . . . . 430--442
Klaus Neymeyr and
Evgueni Ovtchinnikov and
Ming Zhou Convergence Analysis of Gradient
Iterations for the Symmetric Eigenvalue
Problem . . . . . . . . . . . . . . . . 443--456
Minghua Lin and
Gord Sinnamon A Condition for Convexity of a Product
of Positive Definite Quadratic Forms . . 457--462
María I. Bueno and
Fernando de Terán and
Froilán M. Dopico Recovery of Eigenvectors and Minimal
Bases of Matrix Polynomials from
Generalized Fiedler Linearizations . . . 463--483
R. Alam and
S. Bora and
M. Karow and
V. Mehrmann and
J. Moro Perturbation Theory for Hamiltonian
Matrices and the Distance to
Bounded-Realness . . . . . . . . . . . . 484--514
Heinrich Voss and
Kemal Yildiztekin and
Xin Huang Nonlinear Low Rank Modification of a
Symmetric Eigenvalue Problem . . . . . . 515--535
Walter Zulehner Nonstandard Norms and Robust Estimates
for Saddle Point Problems . . . . . . . 536--560
Alwin Stegeman On Uniqueness of the Canonical Tensor
Decomposition with Some Form of Symmetry 561--583
Zhigang Jia and
Musheng Wei A Real-Valued Spectral Decomposition of
the Undamped Gyroscopic System with
Applications . . . . . . . . . . . . . . 584--604
Takanori Maehara and
Kazuo Murota Algorithm for Error-Controlled
Simultaneous Block-Diagonalization of
Matrices . . . . . . . . . . . . . . . . 605--620
M. Eiermann and
O. G. Ernst and
S. Güttel Deflated Restarting for Matrix Functions 621--641
Ren-Cang Li and
Yuji Nakatsukasa and
Ninoslav Truhar and
Shufang Xu Perturbation of Partitioned Hermitian
Definite Generalized Eigenvalue Problems 642--663
Arno Berger and
Theodore P. Hill and
Bahar Kaynar and
Ad Ridder Finite-state Markov Chains Obey
Benford's Law . . . . . . . . . . . . . 665--684
Marc Baboulin and
Serge Gratton A Contribution to the Conditioning of
the Total Least-Squares Problem . . . . 685--699
Alberto Seeger Quadratic Eigenvalue Problems under
Conic Constraints . . . . . . . . . . . 700--721
Roberto Bevilacqua and
Enrico Bozzo and
Gianna M. Del Corso $ q d $-Type Methods for Quasiseparable
Matrices . . . . . . . . . . . . . . . . 722--747
Iveta Hn\vetynková and
Martin Ple\vsinger and
Diana Maria Sima and
Zden\vek Strako\vs and
Sabine Van Huffel The Total Least Squares Problem in $ A X
\approx B $: a New Classification with
the Relationship to the Classical Works 748--770
Lj. Cvetkovi\'c and
V. Kosti\'c and
J. M. Peña Eigenvalue Localization Refinements for
Matrices Related to Positivity . . . . . 771--784
Zheng-Jian Bai and
Marco Donatelli and
Stefano Serra-Capizzano Fast Preconditioners for Total Variation
Deblurring with Antireflective Boundary
Conditions . . . . . . . . . . . . . . . 785--805
Kung-Ching Chang and
Kelly J. Pearson and
Tan Zhang Primitivity, the Convergence of the NQZ
Method, and the Largest Eigenvalue for
Nonnegative Tensors . . . . . . . . . . 806--819
Delin Chu and
Siong Thye Goh and
Y. S. Hung Characterization of All Solutions for
Undersampled Uncorrelated Linear
Discriminant Analysis Problems . . . . . 820--844
Michael Karow $ \mu $-Values and Spectral Value Sets
for Linear Perturbation Classes Defined
by a Scalar Product . . . . . . . . . . 845--865
Grey Ballard and
James Demmel and
Olga Holtz and
Oded Schwartz Minimizing Communication in Numerical
Linear Algebra . . . . . . . . . . . . . 866--901
Elias Jarlebring and
Simen Kvaal and
Wim Michiels Computing all Pairs $ (\lambda, \mu) $
Such That $ \lambda $ is a Double
Eigenvalue of $ A + \mu B $ . . . . . . 902--927
Alex Druinsky and
Sivan Toledo The Growth-Factor Bound for the
Bunch--Kaufman Factorization Is Tight 928--937
Simone Fiori Solving Minimal-Distance Problems over
the Manifold of Real-Symplectic Matrices 938--968
S. Gratton and
Ph. L. Toint and
J. Tshimanga Ilunga Range-Space Variants and Inexact
Matrix-Vector Products in Krylov Solvers
for Linear Systems Arising from Inverse
Problems . . . . . . . . . . . . . . . . 969--986
Ivan Markovsky On the Complex Least Squares Problem
with Constrained Phase . . . . . . . . . 987--992
Daniel B. Szyld and
Fei Xue Efficient Preconditioned Inner Solves
For Inexact Rayleigh Quotient Iteration
And Their Connections To The
Single-Vector Jacobi--Davidson Method 993--1018
Anatoli Juditsky and
Fatma Kilinç karzan and
Arkadi Nemirovski On Low Rank Matrix Approximations with
Applications to Synthesis Problem in
Compressed Sensing . . . . . . . . . . . 1019--1029
Chee Wei Tan and
Shmuel Friedland and
Steven Low Nonnegative Matrix Inequalities and
their Application to Nonconvex Power
Control Optimization . . . . . . . . . . 1030--1055
Nicholas J. Higham and
Lijing Lin A Schur--Padé Algorithm for Fractional
Powers of a Matrix . . . . . . . . . . . 1056--1078
Christopher C. Paige and
Ivo Panayotov Hessenberg Matrix Properties and Ritz
Vectors in the Finite-Precision Lanczos
Tridiagonalization Process . . . . . . . 1079--1094
Tamara G. Kolda and
Jackson R. Mayo Shifted Power Method for Computing
Tensor Eigenpairs . . . . . . . . . . . 1095--1124
Marco Donatelli and
Matteo Semplice and
Stefano Serra-Capizzano Analysis of Multigrid Preconditioning
for Implicit PDE Solvers for Degenerate
Parabolic Equations . . . . . . . . . . 1125--1148
Nicolas Gillis and
François Glineur Low-Rank Matrix Approximation with
Weights or Missing Data Is NP-Hard . . . 1149--1165
Nicola Guglielmi and
Michael L. Overton Fast Algorithms for the Approximation of
the Pseudospectral Abscissa and
Pseudospectral Radius of a Matrix . . . 1166--1192
Zhaosong Lu and
Ting Kei Pong Minimizing Condition Number via Convex
Programming . . . . . . . . . . . . . . 1193--1211
L. M. Carvalho and
S. Gratton and
R. Lago and
X. Vasseur A Flexible Generalized Conjugate
Residual Method with Inner
Orthogonalization and Deflated
Restarting . . . . . . . . . . . . . . . 1212--1235
Qingzhi Yang and
Yuning Yang Further Results for Perron--Frobenius
Theorem for Nonnegative Tensors II . . . 1236--1250
P. G. Martinsson A Fast Randomized Algorithm for
Computing a Hierarchically Semiseparable
Representation of a Matrix . . . . . . . 1251--1274
Andrey Kovalenko and
Trond Mannseth and
Geir Nævdal Error Estimate for the Ensemble Kalman
Filter Analysis Step . . . . . . . . . . 1275--1287
Daniel Kressner and
Christine Tobler Low-Rank Tensor Krylov Subspace Methods
for Parametrized Linear Systems . . . . 1288--1316
Laura Grigori and
James W. Demmel and
Hua Xiang CALU: a Communication Optimal $ L U $
Factorization Algorithm . . . . . . . . 1317--1350
M. Mönnigmann Fast Calculation of Spectral Bounds for
Hessian Matrices on Hyperrectangles . . 1351--1366
Matthew M. Lin Discrete Eckart--Young Theorem for
Integer Matrices . . . . . . . . . . . . 1367--1382
Michael Karow Structured Pseudospectra for Small
Perturbations . . . . . . . . . . . . . 1383--1398
Wim Michiels and
Elias Jarlebring and
Karl Meerbergen Krylov-Based Model Order Reduction of
Time-delay Systems . . . . . . . . . . . 1399--1421
Lars Eldén and
Berkant Savas Perturbation Theory and Optimality
Conditions for the Best Multilinear Rank
Approximation of a Tensor . . . . . . . 1422--1450
Lieven De Lathauwer Blind Separation of Exponential
Polynomials and the Decomposition of a
Tensor in Rank-$ (L_r, L_r, 1) $ Terms 1451--1474
Fred W. Wubs and
Jonas Thies A Robust Two-Level Incomplete
Factorization for (Navier-)Stokes Saddle
Point Matrices . . . . . . . . . . . . . 1475--1499
Cristiano Bocci and
Enrico Carlini and
Fabio Rapallo Perturbation of Matrices and Nonnegative
Rank with a View toward Statistical
Models . . . . . . . . . . . . . . . . . 1500--1512
André M. S. Barreto and
Marcelo D. Fragoso Computing the Stationary Distribution of
a Finite Markov Chain Through Stochastic
Factorization . . . . . . . . . . . . . 1513--1523
Rui Ralha Reliable Eigenvalues of Symmetric
Tridiagonals . . . . . . . . . . . . . . 1524--1536
Paolo Novati Using the Restricted-denominator
Rational Arnoldi Method for Exponential
Integrators . . . . . . . . . . . . . . 1537--1558
Anonymous Erratum: ``Primitivity, the Convergence
of the NQZ Method, and the Largest
Eigenvalue for Nonnegative Tensors''
(SIAM J. Matrix Anal. Appl., \bf 32
(2011), pp. 806--819) . . . . . . . . . 1559--1559
Brian D. Sutton Stable Computation of the CS
Decomposition: Simultaneous
Bidiagonalization . . . . . . . . . . . 1--21
Yuji Nakatsukasa and
Kensuke Aishima and
Ichitaro Yamazaki dqds with Aggressive Early Deflation . . 22--51
Michael L. Stein and
Jie Chen and
Mihai Anitescu Difference Filter Preconditioning for
Large Covariance Matrices . . . . . . . 52--72
Thomas K. Huckle and
Christos Kravvaritis Compact Fourier Analysis for Multigrid
Methods based on Block Symbols . . . . . 73--96
A. Hadjidimos and
M. Lapidakis and
M. Tzoumas On Iterative Solution for Linear
Complementarity Problem with an $ H_+
$-Matrix . . . . . . . . . . . . . . . . 97--110
Xijing Guo and
Sebastian Miron and
David Brie and
Alwin Stegeman Uni-mode and Partial Uniqueness
Conditions for CANDECOMP/PARAFAC of
Three-Way Arrays with Linearly Dependent
Loadings . . . . . . . . . . . . . . . . 111--129
Siegfried M. Rump Verified Bounds for Least Squares
Problems and Underdetermined Linear
Systems . . . . . . . . . . . . . . . . 130--148
Stefan Ragnarsson and
Charles F. Van Loan Block Tensor Unfoldings . . . . . . . . 149--169
Wei-guo Wang and
Wei-chao Wang and
Ren-Cang Li Alternating-directional Doubling
Algorithm for $M$-Matrix Algebraic
Riccati Equations . . . . . . . . . . . 170--194
T. Butler and
P. Constantine and
T. Wildey A Posteriori Error Analysis of
Parameterized Linear Systems Using
Spectral Methods . . . . . . . . . . . . 195--209
O. Curtef and
G. Dirr and
U. Helmke Riemannian Optimization on Tensor
Products of Grassmann Manifolds:
Applications to Generalized
Rayleigh-Quotients . . . . . . . . . . . 210--234
Chun-Hua Guo and
Yueh-Cheng Kuo and
Wen-Wei Lin On a Nonlinear Matrix Equation Arising
in Nano Research . . . . . . . . . . . . 235--262
J. Bailey and
M. A. Iwen and
C. V. Spencer On the Design of Deterministic Matrices
for Fast Recovery of Fourier
Compressible Functions . . . . . . . . . 263--289
Alwin Stegeman Candecomp/Parafac: From Diverging
Components to a Decomposition in Block
Terms . . . . . . . . . . . . . . . . . 291--316
Ian D. Morris A New Sufficient Condition for the
Uniqueness of Barabanov Norms . . . . . 317--324
Xiao Shan Chen and
Wen Li and
Michael K. Ng Perturbation Analysis for Antitriangular
Schur Decomposition . . . . . . . . . . 325--335
Thomas Berger and
Stephan Trenn The Quasi-Kronecker Form For Matrix
Pencils . . . . . . . . . . . . . . . . 336--368
Friederike Voos Result Verification for the Real
Quadratic Eigenvalue Problem . . . . . . 369--387
Jianlin Xia On the Complexity of Some Hierarchical
Structured Matrix Algorithms . . . . . . 388--410
Licio H. Bezerra Vandermonde Factorizations of a Regular
Hankel Matrix and Their Application to
the Computation of Bézier Curves . . . . 411--432
Fei Xue and
Howard C. Elman Fast Inexact Implicitly Restarted
Arnoldi Method for Generalized
Eigenvalue Problems with Spectral
Transformation . . . . . . . . . . . . . 433--459
Yuji Nakatsukasa and
Nicholas J. Higham Backward Stability of Iterations for
Computing the Polar Decomposition . . . 460--479
Mark Embree and
Josef A. Sifuentes and
Kirk M. Soodhalter and
Daniel B. Szyld and
Fei Xue Short-Term Recurrence Krylov Subspace
Methods for Nearly Hermitian Matrices 480--500
Claude Dellacherie and
Servet Martinez and
Jaime San Martin Hadamard Functions that Preserve Inverse
$M$-Matrices . . . . . . . . . . . . . . 501--522
Paul R. Willems and
Bruno Lang Twisted Factorizations and $ q d $-Type
Transformations for the $ \mbox {MR}^3 $
Algorithm --- New Representations and
Analysis . . . . . . . . . . . . . . . . 523--553
Zhen-yun Peng and
Lin Wang and
Jing-jing Peng The Solutions of Matrix Equation $ A X =
B $ Over a Matrix Inequality Constraint 554--568
Changli Liu and
Jungong Xue Complex Nonsymmetric Algebraic Riccati
Equations Arising in Markov Modulated
Fluid Flows . . . . . . . . . . . . . . 569--596
Yueh-Cheng Kuo and
Shih-Feng Shieh A Structure-Preserving Curve for
Symplectic Pairs and Its Applications 597--616
Emanuel Ben-David and
Bala Rajaratnam Positive Definite Completion Problems
for Bayesian Networks . . . . . . . . . 617--638
André Uschmajew Local Convergence of the Alternating
Least Squares Algorithm for Canonical
Tensor Approximation . . . . . . . . . . 639--652
Martin J. Gander and
Sébastien Loisel and
Daniel B. Szyld An Optimal Block Iterative Method and
Preconditioner for Banded Matrices with
Applications to PDEs on Irregular
Domains . . . . . . . . . . . . . . . . 653--680
Jie Huang and
Ronald D. Haynes and
Ting-Zhu Huang Monotonicity of Perturbed Tridiagonal
$M$-Matrices . . . . . . . . . . . . . . 681--700
Peter J. C. Dickinson and
Mirjam Dür Linear-Time Complete Positivity
Detection and Decomposition of Sparse
Matrices . . . . . . . . . . . . . . . . 701--720
Shu-Qian Shen and
Ting-Zhu Huang and
Jian-Song Zhang Augmentation Block Triangular
Preconditioners for Regularized Saddle
Point Problems . . . . . . . . . . . . . 721--741
Vladimir A. Kazeev and
Boris N. Khoromskij Low-Rank Explicit QTT Representation of
the Laplace Operator and Its Inverse . . 742--758
Raf Vandebril and
David S. Watkins A Generalization of the Multishift $ Q R
$ Algorithm . . . . . . . . . . . . . . 759--779
Volker Mehrmann and
Federico Poloni Doubling Algorithms with Permuted
Lagrangian Graph Bases . . . . . . . . . 780--805
Xinzhen Zhang and
Chen Ling and
Liqun Qi The Best Rank-1 Approximation of a
Symmetric Tensor and Related Spherical
Optimization Problems . . . . . . . . . 806--821
Serge Gratton and
Pavel Jiránek and
David Titley-Peloquin On the Accuracy of the Karlson--Waldén
Estimate of the Backward Error for
Linear Least Squares Problems . . . . . 822--836
Jianlin Xia and
Yuanzhe Xi and
Ming Gu A Superfast Structured Solver for
Toeplitz Linear Systems via Randomized
Sampling . . . . . . . . . . . . . . . . 837--858
Peter Benner and
Tobias Breiten Interpolation-Based $ {\cal H}_2 $-Model
Reduction of Bilinear Control Systems 859--885
ShengGuo Li and
Ming Gu and
Cinna Julie Wu and
JianLin Xia New Efficient and Robust HSS Cholesky
Factorization of SPD Matrices . . . . . 886--904
Carlos Beltrán and
Jean-Pierre Dedieu and
Gregorio Malajovich and
Mike Shub Convexity Properties of the Condition
Number II . . . . . . . . . . . . . . . 905--939
Musheng Wei and
Dongmei Shen Minimum Rank Solutions to the Matrix
Approximation Problems in the Spectral
Norm . . . . . . . . . . . . . . . . . . 940--957
Jurjen Duintjer Tebbens and
Gérard Meurant Any Ritz Value Behavior Is Possible for
Arnoldi and for GMRES . . . . . . . . . 958--978
Günter Mayer An Oettli--Prager-Like Theorem for the
Symmetric Solution Set and for Related
Solution Sets . . . . . . . . . . . . . 979--999
Emre Mengi Nearest Linear Systems with Highly
Deficient Reachable Subspaces . . . . . 1000--1017
Luca Chiantini and
Giorgio Ottaviani On Generic Identifiability of
$3$-Tensors of Small Rank . . . . . . . 1018--1037
Paola Favati and
Grazia Lotti and
Ornella Menchi A Divide and Conquer Algorithm for the
Superfast Solution of Toeplitz-like
Systems . . . . . . . . . . . . . . . . 1039--1056
Yuanyuan Liu Perturbation Bounds for the Stationary
Distributions of Markov Chains . . . . . 1057--1074
Zhaojun Bai and
Ren-Cang Li Minimization Principles for the Linear
Response Eigenvalue Problem I: Theory 1075--1100
T. S. Haut and
G. Beylkin Fast and Accurate Con-Eigenvalue
Algorithm for Optimal Rational
Approximations . . . . . . . . . . . . . 1101--1125
John W. Pearson and
Martin Stoll and
Andrew J. Wathen Regularization-Robust Preconditioners
for Time-Dependent PDE-Constrained
Optimization Problems . . . . . . . . . 1126--1152
Pavel Zhlobich Differential $ q d $ Algorithm with
Shifts for Rank-Structured Matrices . . 1153--1171
Evgenija D. Popova Explicit Description of \em AE Solution
Sets for Parametric Linear Systems . . . 1172--1189
Mikael Sòrensen and
Lieven De Lathauwer and
Pierre Comon and
Sylvie Icart and
Luc Deneire Canonical Polyadic Decomposition with a
Columnwise Orthonormal Factor Matrix . . 1190--1213
Carl D. Meyer and
Charles D. Wessell Stochastic Data Clustering . . . . . . . 1214--1236
Mátyás A. Sustik and
Inderjit S. Dhillon On a Zero-Finding Problem Involving the
Matrix Exponential . . . . . . . . . . . 1237--1249
Alwin Stegeman and
Tam T. T. Lam Improved Uniqueness Conditions for
Canonical Tensor Decompositions with
Linearly Dependent Loadings . . . . . . 1250--1271
Eric C. Chi and
Tamara G. Kolda On Tensors, Sparsity, and Nonnegative
Factorizations . . . . . . . . . . . . . 1272--1299
P. Butt\`a and
N. Guglielmi and
S. Noschese Computing the Structured Pseudospectrum
of a Toeplitz Matrix and Its Extreme
Points . . . . . . . . . . . . . . . . . 1300--1319
Russell L. Carden and
Mark Embree Ritz Value Localization for
Non-Hermitian Matrices . . . . . . . . . 1320--1338
Federico Poloni and
Timo Reis A Deflation Approach for Large-Scale
Lur'e Equations . . . . . . . . . . . . 1339--1368
Lars Eldén and
Valeria Simoncini Solving Ill-Posed Linear Systems with
GMRES and a Singular Preconditioner . . 1369--1394
J. Saunderson and
V. Chandrasekaran and
P. A. Parrilo and
A. S. Willsky Diagonal and Low-Rank Matrix
Decompositions, Correlation Matrices,
and Ellipsoid Fitting . . . . . . . . . 1395--1416
Keiichi Morikuni and
Ken Hayami Inner-Iteration Krylov Subspace Methods
for Least Squares Problems . . . . . . . 1--22
Donniell E. Fishkind and
Daniel L. Sussman and
Minh Tang and
Joshua T. Vogelstein and
Carey E. Priebe Consistent Adjacency-Spectral
Partitioning for the Stochastic Block
Model When the Model Parameters Are
Unknown . . . . . . . . . . . . . . . . 23--39
Nicola Guglielmi and
Christian Lubich Low-Rank Dynamics for Computing Extremal
Points of Real Pseudospectra . . . . . . 40--66
Hou-Duo Qi A Semismooth Newton Method for the
Nearest Euclidean Distance Matrix
Problem . . . . . . . . . . . . . . . . 67--93
Thomas Berger and
Stephan Trenn Addition to ``The Quasi-Kronecker Form
for Matrix Pencils'' . . . . . . . . . . 94--101
Kim Batselier and
Philippe Dreesen and
Bart De Moor The Geometry of Multivariate Polynomial
Division and Elimination . . . . . . . . 102--125
Anh-Huy Phan and
Petr Tichavský and
Andrzej Cichocki Low Complexity Damped Gauss--Newton
Algorithms for CANDECOMP/PARAFAC . . . . 126--147
Misha E. Kilmer and
Karen Braman and
Ning Hao and
Randy C. Hoover Third-Order Tensors as Operators on
Matrices: a Theoretical and
Computational Framework with
Applications in Imaging . . . . . . . . 148--172
Nicola Mastronardi and
Paul Van Dooren The Antitriangular Factorization of
Symmetric Matrices . . . . . . . . . . . 173--196
Jianlin Xia Randomized Sparse Direct Solvers . . . . 197--227
W. Kratz and
R. Simon Hilscher A Generalized Index Theorem for Monotone
Matrix-Valued Functions with
Applications to Discrete Oscillation
Theory . . . . . . . . . . . . . . . . . 228--243
Peizhen Zhu and
Merico E. Argentati and
Andrew V. Knyazev Bounds for the Rayleigh Quotient and the
Spectrum of Self-Adjoint Operators . . . 244--256
Prathapasinghe Dharmawansa and
Matthew R. McKay and
Yang Chen Distributions of Demmel and Related
Condition Numbers . . . . . . . . . . . 257--279
Ren-Cang Li and
Yuji Nakatsukasa and
Ninoslav Truhar and
Shufang Xu Erratum: ``Perturbation of Partitioned
Hermitian Definite Generalized
Eigenvalue Problems'' . . . . . . . . . 280--281
Martin H. Gutknecht and
Jens-Peter M. Zemke Eigenvalue Computations Based on IDR . . 283--311
Françoise Tisseur and
Ion Zaballa Triangularizing Quadratic Matrix
Polynomials . . . . . . . . . . . . . . 312--337
Claude-Pierre Jeannerod and
Siegfried M. Rump Improved Error Bounds for Inner Products
in Floating-Point Arithmetic . . . . . . 338--344
Kamer Kaya and
Bora Uçar Constructing Elimination Trees for
Sparse Unsymmetric Matrices . . . . . . 345--354
Naomi Shaked-Monderer and
Immanuel M. Bomze and
Florian Jarre and
Werner Schachinger On the $ c p $-Rank and Minimal $ c p $
Factorizations of a Completely Positive
Matrix . . . . . . . . . . . . . . . . . 355--368
Tsung-Ming Huang and
Han-En Hsieh and
Wen-Wei Lin and
Weichung Wang Eigendecomposition of the Discrete
Double-Curl Operator with Application to
Fast Eigensolver for Three-Dimensional
Photonic Crystals . . . . . . . . . . . 369--391
Zhaojun Bai and
Ren-Cang Li Minimization Principles for the Linear
Response Eigenvalue Problem II:
Computation . . . . . . . . . . . . . . 392--416
Brian D. Sutton Divide and Conquer the CS Decomposition 417--444
P.-L. Giscard and
S. J. Thwaite and
D. Jaksch Evaluating Matrix Functions by
Resummations on Graphs: The Method of
Path-Sums . . . . . . . . . . . . . . . 445--469
Christian Lubich and
Thorsten Rohwedder and
Reinhold Schneider and
Bart Vandereycken Dynamical Approximation by Hierarchical
Tucker and Tensor-Train Tensors . . . . 470--494
André Gaul and
Martin H. Gutknecht and
Jörg Liesen and
Reinhard Nabben A Framework for Deflated and Augmented
Krylov Subspace Methods . . . . . . . . 495--518
Luca Dieci and
Alessandra Papini and
Alessandro Pugliese Approximating Coalescing Points for
Eigenvalues of Hermitian Matrices of
Three Parameters . . . . . . . . . . . . 519--541
M. Brazell and
N. Li and
C. Navasca and
C. Tamon Solving Multilinear Systems via Tensor
Inversion . . . . . . . . . . . . . . . 542--570
M. Arioli Generalized Golub--Kahan
Bidiagonalization and Stopping Criteria 571--592
Sergey Dolgov and
Boris Khoromskij Two-Level QTT--Tucker Format for
Optimized Tensor Calculus . . . . . . . 593--623
Alwin Stegeman A Three-Way Jordan Canonical Form as
Limit of Low-Rank Tensor Approximations 624--650
Mariya Ishteva and
P.-A. Absil and
Paul Van Dooren Jacobi Algorithm for the Best Low
Multilinear Rank Approximation of
Symmetric Tensors . . . . . . . . . . . 651--672
Ajda Fosner and
Zejun Huang and
Chi-Kwong Li and
Nung-Sing Sze Linear Maps Preserving Ky Fan Norms and
Schatten Norms of Tensor Products of
Matrices . . . . . . . . . . . . . . . . 673--685
Puduru Viswanadha Reddy and
Jacob Christiaan Engwerda Feedback Properties of Descriptor
Systems Using Matrix Projectors and
Applications to Descriptor Differential
Games . . . . . . . . . . . . . . . . . 686--708
Nicola Guglielmi and
Mert Gürbüzbalaban and
Michael L. Overton Fast Approximation of the $ H_\infty $
Norm via Optimization over Spectral
Value Sets . . . . . . . . . . . . . . . 709--737
Han Cheng Lie and
Konstantin Fackeldey and
Marcus Weber A Square Root Approximation of
Transition Rates for a Markov State
Model . . . . . . . . . . . . . . . . . 738--756
Matan Gavish and
Boaz Nadler Normalized Cuts Are Approximately
Inverse Exit Times . . . . . . . . . . . 757--772
Anastasios Zouzias and
Nikolaos M. Freris Randomized Extended Kaczmarz for Solving
Least Squares . . . . . . . . . . . . . 773--793
Bruno Iannazzo and
Carlo Manasse A Schur Logarithmic Algorithm for
Fractional Powers of Matrices . . . . . 794--813
Ivan Markovsky and
Konstantin Usevich Structured Low-Rank Approximation with
Missing Data . . . . . . . . . . . . . . 814--830
Claude Dellacherie and
Servet Martinez and
Jaime San Martin The Class of Inverse $M$-Matrices
Associated to Random Walks . . . . . . . 831--854
Ignat Domanov and
Lieven De Lathauwer On the Uniqueness of the Canonical
Polyadic Decomposition of Third-Order
Tensors --- Part I: Basic Results and
Uniqueness of One Factor Matrix . . . . 855--875
Ignat Domanov and
Lieven De Lathauwer On the Uniqueness of the Canonical
Polyadic Decomposition of Third-Order
Tensors --- Part II: Uniqueness of the
Overall Decomposition . . . . . . . . . 876--903
I. Ben Gharbia and
J. Ch. Gilbert An Algorithmic Characterization of
$P$-Matricity . . . . . . . . . . . . . 904--916
Iveta Hnetynková and
Martin Plesinger and
Zdenek Strakos The Core Problem within a Linear
Approximation Problem $ A X \approx B $
with Multiple Right-Hand Sides . . . . . 917--931
Yongdo Lim Riemannian Distances between Geometric
Means . . . . . . . . . . . . . . . . . 932--945
Maryam Fazel and
Ting Kei Pong and
Defeng Sun and
Paul Tseng Hankel Matrix Rank Minimization with
Applications to System Identification
and Realization . . . . . . . . . . . . 946--977
Lee Altenberg On the Ordering of Spectral Radius
Product $ r(\mathbf {A}) r(\mathbf {AD})
$ versus $ r(\mathbf {A}^2 \mathbf {D})
$ and Related Applications . . . . . . . 978--998
Y. Nesterov and
V. Y. Protasov Optimizing the Spectral Radius . . . . . 999--1013
Elizabeth S. Allman and
Peter D. Jarvis and
John A. Rhodes and
Jeremy G. Sumner Tensor Rank, Invariants, Inequalities,
and Applications . . . . . . . . . . . . 1014--1045
A. Frommer and
K. Kahl and
Th. Lippert and
H. Rittich $2$-Norm Error Bounds and Estimates for
Lanczos Approximations to Linear Systems
and Rational Matrix Functions . . . . . 1046--1065
Josef A. Sifuentes and
Mark Embree and
Ronald B. Morgan GMRES Convergence for Perturbed
Coefficient Matrices, with Application
to Approximate Deflation Preconditioning 1066--1088
Jiang Qian and
Alan L. Andrew and
Delin Chu and
Roger C. E. Tan Computing Derivatives of Repeated
Eigenvalues and Corresponding
Eigenvectors of Quadratic Eigenvalue
Problems . . . . . . . . . . . . . . . . 1089--1111
Nieves Castro-González and
Johan Ceballos and
Froilán M. Dopico and
Juan M. Molera Accurate Solution of Structured Least
Squares Problems via Rank-Revealing
Decompositions . . . . . . . . . . . . . 1112--1128
Tiexiang Li and
Eric King-wah Chu and
Yueh-Cheng Kuo and
Wen-Wei Lin Solving Large-Scale Nonsymmetric
Algebraic Riccati Equations by Doubling 1129--1147
Artem Napov Conditioning Analysis of Incomplete
Cholesky Factorizations with Orthogonal
Dropping . . . . . . . . . . . . . . . . 1148--1173
V. Yu. Protasov Classification of $k$-Primitive Sets of
Matrices . . . . . . . . . . . . . . . . 1174--1188
Nicolas Gillis Robustness Analysis of Hottopixx, a
Linear Programming Model for Factoring
Nonnegative Matrices . . . . . . . . . . 1189--1212
J. L. Mead and
C. C. Hammerquist $ \chi^2 $ Tests for the Choice of the
Regularization Parameter in Nonlinear
Inverse Problems . . . . . . . . . . . . 1213--1230
C. Effenberger Robust Successive Computation of
Eigenpairs for Nonlinear Eigenvalue
Problems . . . . . . . . . . . . . . . . 1231--1256
Serge Gratton and
David Titley-Peloquin and
Jean Tshimanga Ilunga Sensitivity and Conditioning of the
Truncated Total Least Squares Solution 1257--1276
Piers W. Lawrence Fast Reduction of Generalized Companion
Matrix Pairs for Barycentric Lagrange
Interpolants . . . . . . . . . . . . . . 1277--1300
Christos Boutsidis and
Alex Gittens Improved Matrix Algorithms via the
Subsampled Randomized Hadamard Transform 1301--1340
Nicholas J. Higham and
Lijing Lin An Improved Schur--Padé Algorithm for
Fractional Powers of a Matrix and Their
Fréchet Derivatives . . . . . . . . . . . 1341--1360
Jiawei Chiu and
Laurent Demanet Sublinear Randomized Algorithms for
Skeleton Decompositions . . . . . . . . 1361--1383
Zachary B. Charles and
Miriam Farber and
Charles R. Johnson and
Lee Kennedy-Shaffer Nonpositive Eigenvalues of Hollow,
Symmetric, Nonnegative Matrices . . . . 1384--1400
Amal Khabou and
James W. Demmel and
Laura Grigori and
Ming Gu $ L U $ Factorization with Panel Rank
Revealing Pivoting and Its Communication
Avoiding Version . . . . . . . . . . . . 1401--1429
J. D. Hogg and
J. A. Scott Optimal Weighted Matchings for
Rank-Deficient Sparse Matrices . . . . . 1431--1447
Stephen D. Shank and
Valeria Simoncini Krylov Subspace Methods for Large-Scale
Constrained Sylvester Equations . . . . 1448--1463
Haim Avron and
Christos Boutsidis Faster Subset Selection for Matrices and
Applications . . . . . . . . . . . . . . 1464--1499
Vance Faber and
Jörg Liesen and
Petr Tichý Properties of Worst-Case GMRES . . . . . 1500--1519
Tom Bella and
Vadim Olshevsky and
Michael Stewart Nested Product Decomposition of
Quasiseparable Matrices . . . . . . . . 1520--1555
Zhaosong Lu and
Ting Kei Pong Computing Optimal Experimental Designs
via Interior Point Method . . . . . . . 1556--1580
Yisheng Song and
Liqun Qi Spectral Properties of Positively
Homogeneous Operators Induced by Higher
Order Tensors . . . . . . . . . . . . . 1581--1595
I. Pultarová Fourier Analysis of the Aggregation
Based Algebraic Multigrid for Stochastic
Matrices . . . . . . . . . . . . . . . . 1596--1610
Afonso S. Bandeira and
Amit Singer and
Daniel A. Spielman A Cheeger Inequality for the Graph
Connection Laplacian . . . . . . . . . . 1611--1630
Nguyen Huu Du and
Vu Hoang Linh and
Volker Mehrmann and
Do Duc Thuan Stability and Robust Stability of Linear
Time-Invariant Delay
Differential-Algebraic Equations . . . . 1631--1654
C. Fenu and
D. Martin and
L. Reichel and
G. Rodriguez Block Gauss and Anti-Gauss Quadrature
with Application to Networks . . . . . . 1655--1684
Howard C. Elman and
Minghao Wu Lyapunov Inverse Iteration for Computing
a Few Rightmost Eigenvalues of Large
Generalized Eigenvalue Problems . . . . 1685--1707
Dario A. Bini and
Vanni Noferini and
Meisam Sharify Locating the Eigenvalues of Matrix
Polynomials . . . . . . . . . . . . . . 1708--1727
David Bindel and
Amanda Hood Localization Theorems for Nonlinear
Eigenvalue Problems . . . . . . . . . . 1728--1749
Robert Luce and
Esmond G. Ng On the Minimum FLOPs Problem in the
Sparse Cholesky Factorization . . . . . 1--21
Erin Carson and
James Demmel A Residual Replacement Strategy for
Improving the Maximum Attainable
Accuracy of $s$-Step . . . . . . . . . . 22--43
Yuanzhe Xi and
Jianlin Xia and
Stephen Cauley and
Venkataramanan Balakrishnan Superfast and Stable Structured Solvers
for Toeplitz Least Squares via
Randomized Sampling . . . . . . . . . . 44--72
Guyan Ni and
Liqun Qi and
Minru Bai Geometric Measure of Entanglement and
$U$-Eigenvalues of Tensors . . . . . . . 73--87
Mary Aprahamian and
Nicholas J. Higham The Matrix Unwinding Function, with an
Application to Computing the Matrix
Exponential . . . . . . . . . . . . . . 88--109
Serge Gratton and
David Titley-Peloquin and
Philippe Toint and
Jean Tshimanga Ilunga Differentiating the Method of Conjugate
Gradients . . . . . . . . . . . . . . . 110--126
Anwa Zhou and
Jinyan Fan The CP-Matrix Completion Problem . . . . 127--142
Yvan Notay A New Analysis of Block Preconditioners
for Saddle Point Problems . . . . . . . 143--173
Jurjen Duintjer Tebbens and
Miroslav Tuma On Incremental Condition Estimators in
the $2$-Norm . . . . . . . . . . . . . . 174--197
Rüdiger Borsdorf An Algorithm for Finding an Optimal
Projection of a Symmetric Matrix onto a
Diagonal Matrix . . . . . . . . . . . . 198--224
Donald Goldfarb and
Zhiwei (Tony) Qin Robust Low-Rank Tensor Recovery: Models
and Algorithms . . . . . . . . . . . . . 225--253
Peter Lancaster and
Ion Zaballa On the Inverse Symmetric Quadratic
Eigenvalue Problem . . . . . . . . . . . 254--278
Åke Björck Stability of Two Direct Methods for
Bidiagonalization and Partial Least
Squares . . . . . . . . . . . . . . . . 279--291
Daniel Kressner and
Bart Vandereycken Subspace Methods for Computing the
Pseudospectral Abscissa and the
Stability Radius . . . . . . . . . . . . 292--313
Catherine E. Powell and
Elisabeth Ullmann Erratum: Preconditioning Stochastic
Galerkin Saddle Point Systems . . . . . 314--315
Meiyue Shao and
Weiguo Gao and
Jungong Xue Aggressively Truncated Taylor Series
Method for Accurate Computation of
Exponentials of Essentially Nonnegative
Matrices . . . . . . . . . . . . . . . . 317--338
J. Pestana and
A. J. Wathen The Antitriangular Factorization of
Saddle Point Matrices . . . . . . . . . 339--353
Ping Tak Peter Tang and
Eric Polizzi FEAST as a Subspace Iteration
Eigensolver Accelerated by Approximate
Spectral Projection . . . . . . . . . . 354--390
Raphaël M. Jungers and
Antonio Cicone and
Nicola Guglielmi Lifted Polytope Methods for Computing
the Joint Spectral Radius . . . . . . . 391--410
Elias Jarlebring and
Karl Meerbergen and
Wim Michiels Computing a Partial Schur Factorization
of Nonlinear Eigenvalue Problems Using
the Infinite Arnoldi Method . . . . . . 411--436
Liping Zhang and
Liqun Qi and
Guanglu Zhou $M$-Tensors and Some Applications . . . 437--452
Shreemayee Bora and
Michael Karow and
Christian Mehl and
Punit Sharma Structured Eigenvalue Backward Errors of
Matrix Pencils and Polynomials with
Hermitian and Related Structures . . . . 453--475
V. Druskin and
V. Simoncini and
M. Zaslavsky Adaptive Tangential Interpolation in
Rational Krylov Subspaces for MIMO
Dynamical Systems . . . . . . . . . . . 476--498
Linghui Zeng and
Yangfeng Su A Backward Stable Algorithm for
Quadratic Eigenvalue Problems . . . . . 499--516
Jennifer Pestana On the Eigenvalues and Eigenvectors of
Block Triangular Preconditioned Block
Matrices . . . . . . . . . . . . . . . . 517--525
Christopher C. Paige and
Wolfgang Wülling Properties of a Unitary Matrix Obtained
from a Sequence of Normalized Vectors 526--545
Xin Liu and
Xiao Wang and
Zaiwen Wen and
Yaxiang Yuan On the Convergence of the
Self-Consistent Field Iteration in
Kohn--Sham Density Functional Theory . . 546--558
Thomas Mach and
Raf Vandebril On Deflations in Extended $ Q R $
Algorithms . . . . . . . . . . . . . . . 559--579
A. Daniilidis and
D. Drusvyatskiy and
A. S. Lewis Orthogonal Invariance and
Identifiability . . . . . . . . . . . . 580--598
Michael Karow and
Daniel Kressner On a Perturbation Bound for Invariant
Subspaces of Matrices . . . . . . . . . 599--618
Melina A. Freitag and
Alastair Spence and
Paul Van Dooren Calculating the $ H_{\infty } $-norm
Using the Implicit Determinant Method 619--635
Ignat Domanov and
Lieven De Lathauwer Canonical Polyadic Decomposition of
Third-Order Tensors: Reduction to
Generalized Eigenvalue Decomposition . . 636--660
Andreas Frommer and
Stefan Güttel and
Marcel Schweitzer Efficient and Stable Arnoldi Restarts
for Matrix Functions Based on Quadrature 661--683
Siegfried M. Rump and
Claude-Pierre Jeannerod Improved Backward Error Bounds for $ L U
$ and Cholesky Factorizations . . . . . 684--698
Emre Mengi and
E. Alper Yildirim and
Mustafa Kiliç Numerical Optimization of Eigenvalues of
Hermitian Matrix Functions . . . . . . . 699--724
Kenneth L. Ho and
Leslie Greengard A Fast Semidirect Least Squares
Algorithm for Hierarchically Block
Separable Matrices . . . . . . . . . . . 725--748
Vladimir Yu. Protasov and
Dmitrii O. Logofet Rank-One Corrections of Nonnegative
Matrices, With an Application to Matrix
Population Models . . . . . . . . . . . 749--764
Lei-Hong Zhang and
Jungong Xue and
Ren-Cang Li Rayleigh--Ritz Approximation For the
Linear Response Eigenvalue Problem . . . 765--782
J. D. Hogg and
J. A. Scott Compressed Threshold Pivoting for Sparse
Symmetric Indefinite Systems . . . . . . 783--817
Michael Karow and
Daniel Kressner and
Emre Mengi Nonlinear Eigenvalue Problems with
Specified Eigenvalues . . . . . . . . . 819--834
Daniel A. Spielman and
Shang-Hua Teng Nearly Linear Time Algorithms for
Preconditioning and Solving Symmetric,
Diagonally Dominant Linear Systems . . . 835--885
N. Vannieuwenhoven and
J. Nicaise and
R. Vandebril and
K. Meerbergen On Generic Nonexistence of the
Schmidt--Eckart--Young Decomposition for
Complex Tensors . . . . . . . . . . . . 886--903
Megan Dailey and
Froilán M. Dopico and
Qiang Ye A New Perturbation Bound for the LDU
Factorization of Diagonally Dominant
Matrices . . . . . . . . . . . . . . . . 904--930
Philip A. Knight and
Daniel Ruiz and
Bora Uçar A Symmetry Preserving Algorithm for
Matrix Scaling . . . . . . . . . . . . . 931--955
Lu-Bin Cui and
Wen Li and
Michael K. Ng Birkhoff--von Neumann Theorem for
Multistochastic Tensors . . . . . . . . 956--973
Yuanzhe Xi and
Jianlin Xia and
Raymond Chan A Fast Randomized Eigensolver with
Structured LDL Factorization Update . . 974--996
Dario Fasino and
Francesco Tudisco An Algebraic Analysis of the Graph
Modularity . . . . . . . . . . . . . . . 997--1018
Nicholas J. Higham and
Samuel D. Relton Higher Order Fréchet Derivatives of
Matrix Functions and the Level-$2$
Condition Number . . . . . . . . . . . . 1019--1037
Shengguo Li and
Ming Gu and
Lizhi Cheng and
Xuebin Chi and
Meng Sun An Accelerated Divide-and-Conquer
Algorithm for the Bidiagonal SVD Problem 1038--1057
Liqi Wang and
Moody T. Chu On the Global Convergence of the
Alternating Least Squares Method for
Rank-One Approximation to Generic
Tensors . . . . . . . . . . . . . . . . 1058--1072
El Houcine Bergou and
Serge Gratton and
Jean Tshimanga The Exact Condition Number of the
Truncated Singular Value Solution of a
Linear Ill-Posed Problem . . . . . . . . 1073--1085
Mansoor Rezghi and
S. Mohammad Hosseini and
Lars Eldén Best Kronecker Product Approximation of
the Blurring Operator in Three
Dimensional Image Restoration Problems 1086--1104
Eugene Vecharynski and
Yousef Saad Fast Updating Algorithms for Latent
Semantic Indexing . . . . . . . . . . . 1105--1131
Patrizio Neff and
Yuji Nakatsukasa and
Andreas Fischle A Logarithmic Minimization Property of
the Unitary Polar Factor in the Spectral
and Frobenius Norms . . . . . . . . . . 1132--1154
Jiawang Nie and
Li Wang Semidefinite Relaxations for Best
Rank-$1$ Tensor Approximations . . . . . 1155--1179
Mariya Ishteva and
Konstantin Usevich and
Ivan Markovsky Factorization Approach to Structured
Low-Rank Approximation with Applications 1180--1204
Shinya Miyajima Fast Enclosure for All Eigenvalues and
Invariant Subspaces in Generalized
Eigenvalue Problems . . . . . . . . . . 1205--1225
Liqun Qi and
Changqing Xu and
Yi Xu Nonnegative Tensor Factorization,
Completely Positive Tensors, and a
Hierarchical Elimination Algorithm . . . 1227--1241
Kim Batselier and
Philippe Dreesen and
Bart De Moor The Canonical Decomposition of $
\mathcal {C}^n_d $ and Numerical Gröbner
and Border Bases . . . . . . . . . . . . 1242--1264
Luca Chiantini and
Giorgio Ottaviani and
Nick Vannieuwenhoven An Algorithm For Generic and Low-Rank
Specific Identifiability of Complex
Tensors . . . . . . . . . . . . . . . . 1265--1287
Neville J. Ford and
Dmitry V. Savostyanov and
Nickolai L. Zamarashkin On the Decay of the Elements of Inverse
Triangular Toeplitz Matrices . . . . . . 1288--1302
Megan Dailey and
Froilán M. Dopico and
Qiang Ye Relative Perturbation Theory for
Diagonally Dominant Matrices . . . . . . 1303--1328
Nick Gould and
Dominique Orban and
Tyrone Rees Projected Krylov Methods for
Saddle-Point Systems . . . . . . . . . . 1329--1343
Antti Koskela and
Alexander Ostermann A Moment-Matching Arnoldi Iteration for
Linear Combinations of $ \varphi $
Functions . . . . . . . . . . . . . . . 1344--1363
Grey Ballard and
Dulceneia Becker and
James Demmel and
Jack Dongarra and
Alex Druinsky and
Inon Peled and
Oded Schwartz and
Sivan Toledo and
Ichitaro Yamazaki Communication-Avoiding
Symmetric-Indefinite Factorization . . . 1364--1406
Nicola Guglielmi and
Daniel Kressner and
Christian Lubich Computing Extremal Points of Symplectic
Pseudospectra and Solving Symplectic
Matrix Nearness Problems . . . . . . . . 1407--1428
Andrii Dmytryshyn and
Bo Kågström Orbit Closure Hierarchies of
Skew-symmetric Matrix Pencils . . . . . 1429--1443
Martin H. Gutknecht Deflated and Augmented Krylov Subspace
Methods: a Framework for Deflated BiCG
and Related Solvers . . . . . . . . . . 1444--1466
Tanja Göckler and
Volker Grimm Uniform Approximation of $ \varphi
$-Functions in Exponential Integrators
by a Rational Krylov Subspace Method
with Simple Poles . . . . . . . . . . . 1467--1489
Ilse C. F. Ipsen and
Thomas Wentworth The Effect of Coherence on Sampling from
Matrices with Orthonormal Columns, and
Preconditioned Least Squares Problems 1490--1520
Giorgio Ottaviani and
Pierre-Jean Spaenlehauer and
Bernd Sturmfels Exact Solutions in Structured Low-Rank
Approximation . . . . . . . . . . . . . 1521--1542
J. H. de M. Goulart and
G. Favier An Algebraic Solution for the
Candecomp/PARAFAC Decomposition with
Circulant Factors . . . . . . . . . . . 1543--1562
Tamara G. Kolda and
Jackson R. Mayo An Adaptive Shifted Power Method for
Computing Generalized Tensor Eigenpairs 1563--1581
Chun-Feng Cui and
Yu-Hong Dai and
Jiawang Nie All Real Eigenvalues of Symmetric
Tensors . . . . . . . . . . . . . . . . 1582--1601
Andreas Frommer and
Stefan Güttel and
Marcel Schweitzer Convergence of Restarted Krylov Subspace
Methods for Stieltjes Functions of
Matrices . . . . . . . . . . . . . . . . 1602--1624
E. Agullo and
L. Giraud and
Y.-F. Jing Block GMRES Method with Inexact
Breakdowns and Deflated Restarting . . . 1625--1651
Liqi Wang and
Moody T. Chu and
Bo Yu Orthogonal Low Rank Tensor
Approximation: Alternating Least Squares
Method and Its Global Convergence . . . 1--19
Immanuel M. Bomze and
Werner Schachinger and
Reinhard Ullrich New Lower Bounds and Asymptotics for the
$ c p$-Rank . . . . . . . . . . . . . . 20--37
Nicola Guglielmi and
Michael L. Overton and
G. W. Stewart An Efficient Algorithm for Computing the
Generalized Null Space Decomposition . . 38--54
James W. Demmel and
Laura Grigori and
Ming Gu and
Hua Xiang Communication Avoiding Rank Revealing $
Q R $ Factorization with Column Pivoting 55--89
Michael McCourt and
Barry Smith and
Hong Zhang Sparse Matrix-Matrix Products Executed
Through Coloring . . . . . . . . . . . . 90--109
John T. Holodnak and
Ilse C. F. Ipsen Randomized Approximation of the Gram
Matrix: Exact Computation and
Probabilistic Bounds . . . . . . . . . . 110--137
Vanni Noferini and
Meisam Sharify and
Françoise Tisseur Tropical Roots as Approximations to
Eigenvalues of Matrix Polynomials . . . 138--157
Rongrong Wang Singular Vector Perturbation Under
Gaussian Noise . . . . . . . . . . . . . 158--177
Volker Mehrmann and
Do Duc Thuan Stability Analysis of Implicit
Difference Equations Under Restricted
Perturbations . . . . . . . . . . . . . 178--202
Ruey-Lin Chern and
Han-En Hsieh and
Tsung-Ming Huang and
Wen-Wei Lin and
Weichung Wang Singular Value Decompositions for
Single-Curl Operators in
Three-Dimensional Maxwell's Equations
for Complex Media . . . . . . . . . . . 203--224
Keiichi Morikuni and
Ken Hayami Convergence of Inner-Iteration GMRES
Methods for Rank-Deficient Least Squares
Problems . . . . . . . . . . . . . . . . 225--250
Leo Taslaman An Algorithm for Quadratic Eigenproblems
with Low Rank Damping . . . . . . . . . 251--272
J. Pestana and
A. J. Wathen A Preconditioned MINRES Method for
Nonsymmetric Toeplitz Matrices . . . . . 273--288
Daeshik Choi and
Anne Greenbaum Roots of Matrices in the Study of GMRES
Convergence and Crouzeix's Conjecture 289--301
Fernando De Terán and
Froilán M. Dopico and
Paul Van Dooren Matrix Polynomials with Completely
Prescribed Eigenstructure . . . . . . . 302--328
Sylvain Arguill\`ere Approximation of Sequences of Symmetric
Matrices with the Symmetric Rank-One
Algorithm and Applications . . . . . . . 329--347
Youngmi Hur and
Kasso A. Okoudjou Scaling Laplacian Pyramids . . . . . . . 348--365
Ron Estrin and
Chen Greif On Nonsingular Saddle-Point Systems with
a Maximally Rank Deficient Leading Block 367--384
Siegfried M. Rump The Componentwise Structured and
Unstructured Backward Errors Can be
Arbitrarily Far Apart . . . . . . . . . 385--392
Shreemayee Bora and
Michael Karow and
Christian Mehl and
Punit Sharma Structured Eigenvalue Backward Errors of
Matrix Pencils and Polynomials with
Palindromic Structures . . . . . . . . . 393--416
Iveta Hnetynková and
Martin Plesinger and
Zdenek Strakos Band Generalization of the Golub--Kahan
Bidiagonalization, Generalized Jacobi
Matrices, and the Core Problem . . . . . 417--434
Vladimir R. Kosti\'c and
Agnieszka Mi\kedlar and
Jeroen J. Stolwijk On Matrix Nearness Problems: Distance to
Delocalization . . . . . . . . . . . . . 435--460
Leo Taslaman Strongly Damped Quadratic Matrix
Polynomials . . . . . . . . . . . . . . 461--475
Rong Huang and
Delin Chu Relative Perturbation Analysis for
Eigenvalues and Singular Values of
Totally Nonpositive Matrices . . . . . . 476--495
Mikael Sòrensen and
Lieven De Lathauwer Coupled Canonical Polyadic
Decompositions and (Coupled)
Decompositions in Multilinear Rank-$
(L_r, n, L_r, n, 1) $ Terms --- Part I:
Uniqueness . . . . . . . . . . . . . . . 496--522
P. Butt\`a and
N. Guglielmi and
M. Manetta and
S. Noschese Differential Equations for
Real-Structured Defectivity Measures . . 523--548
Garret Flagg and
Serkan Gugercin Multipoint Volterra Series Interpolation
and $ \mathcal {H}_2 $ Optimal Model
Reduction of Bilinear Systems . . . . . 549--579
Andrii Dmytryshyn and
Bo Kågström Coupled Sylvester-type Matrix Equations
and Block Diagonalization . . . . . . . 580--593
Philipp Bader and
Sergio Blanes and
Muaz Seydaoglu The Scaling, Splitting, and Squaring
Method for the Exponential of Perturbed
Matrices . . . . . . . . . . . . . . . . 594--614
Evgenija D. Popova Solvability of Parametric Interval
Linear Systems of Equations and
Inequalities . . . . . . . . . . . . . . 615--633
N. Guglielmi and
M. Zennaro Canonical Construction of Polytope
Barabanov Norms and Antinorms for Sets
of Matrices . . . . . . . . . . . . . . 634--655
Jonathan Baker and
Mark Embree and
John Sabino Fast Singular Value Decay for Lyapunov
Solutions with Nonnormal Coefficients 656--668
Massimiliano Fasi and
Nicholas J. Higham and
Bruno Iannazzo An Algorithm for the Matrix Lambert $W$
Function . . . . . . . . . . . . . . . . 669--685
Michele Benzi and
Christine Klymko On the Limiting Behavior of
Parameter-Dependent Network Centrality
Measures . . . . . . . . . . . . . . . . 686--706
Hua Dai and
Zhong-Zhi Bai and
Ying Wei On the Solvability Condition and
Numerical Algorithm for the
Parameterized Generalized Inverse
Eigenvalue Problem . . . . . . . . . . . 707--726
M. Rozlozník and
F. Okulicka-D\luzewska and
A. Smoktunowicz Cholesky-Like Factorization of Symmetric
Indefinite Matrices and
Orthogonalization with Respect to
Bilinear Forms . . . . . . . . . . . . . 727--751
Zhi Zhao and
Zheng-Jian Bai and
Xiao-Qing Jin A Riemannian Newton Algorithm for
Nonlinear Eigenvalue Problems . . . . . 752--774
Yao-Lin Jiang and
Xu Kong On the Uniqueness and Perturbation to
the Best Rank-One Approximation of a
Tensor . . . . . . . . . . . . . . . . . 775--792
Erin Carson and
James W. Demmel Accuracy of the $s$-Step Lanczos Method
for the Symmetric Eigenproblem in Finite
Precision . . . . . . . . . . . . . . . 793--819
Roel Van Beeumen and
Karl Meerbergen and
Wim Michiels Compact Rational Krylov Methods for
Nonlinear Eigenvalue Problems . . . . . 820--838
Yunfeng Cai and
Decai Shi and
Shufang Xu A Matrix Polynomial Spectral Approach
for General Joint Block Diagonalization 839--863
Philippe Dreesen and
Mariya Ishteva and
Johan Schoukens Decoupling Multivariate Polynomials
Using First-Order Information and Tensor
Decompositions . . . . . . . . . . . . . 864--879
Jorge Delgado and
J. M. Penña Accurate Computations with Collocation
Matrices of $q$-Bernstein Polynomials 880--893
Mario Berljafa and
Stefan Güttel Generalized Rational Krylov
Decompositions with an Application to
Rational Approximation . . . . . . . . . 894--916
Erik Thiede and
Brian Van Koten and
Jonathan Weare Sharp Entrywise Perturbation Bounds for
Markov Chains . . . . . . . . . . . . . 917--941
Jared L. Aurentz and
Thomas Mach and
Raf Vandebril and
David S. Watkins Fast and Backward Stable Computation of
Roots of Polynomials . . . . . . . . . . 942--973
Charles F. Van Loan and
Joseph P. Vokt Approximating Matrices with Multiple
Symmetries . . . . . . . . . . . . . . . 974--993
Namgil Lee and
Andrzej Cichocki Estimating a Few Extreme Singular Values
and Vectors for Large-Scale Matrices in
Tensor Train Format . . . . . . . . . . 994--1014
Mikael Sòrensen and
Ignat Domanov and
Lieven De Lathauwer Coupled Canonical Polyadic
Decompositions and (Coupled)
Decompositions in Multilinear Rank-$
(L_{r, n}, L_{r, n}, 1) $ Terms --- Part
II: Algorithms . . . . . . . . . . . . . 1015--1045
R. Bevilacqua and
G. M. Del Corso and
L. Gemignani A CMV-Based Eigensolver for Companion
Matrices . . . . . . . . . . . . . . . . 1046--1068
Sheng Chen and
Yunbo Tian Note on ``On the Singular `Vectors' of
the Lyapunov Operator'' by R. Byers and
S. Nash . . . . . . . . . . . . . . . . 1069--1072
Weiyang Ding and
Yimin Wei Generalized Tensor Eigenvalue Problems 1073--1099
Carlo Garoni and
Stefano Serra-Capizzano and
Debora Sesana Spectral Analysis and Spectral Symbol of
$d$-variate $ \mathbb {Q_{\bf p}}$
Lagrangian FEM Stiffness Matrices . . . 1100--1128
Yuan Xu Generalized Characteristic Polynomials
and Gaussian Cubature Rules . . . . . . 1129--1142
John T. Holodnak and
Ilse C. F. Ipsen and
Thomas Wentworth Conditioning of Leverage Scores and
Computation by $ Q R $ Decomposition . . 1143--1163
Meik Dörpinghaus and
Norbert Gaffke and
Lorens A. Imhof and
Rudolf Mathar A Log-Det Inequality for Random Matrices 1164--1179
Sungkyu Jung and
Armin Schwartzman and
David Groisser Scaling-Rotation Distance and
Interpolation of Symmetric
Positive-Definite Matrices . . . . . . . 1180--1201
Richard A. Brualdi and
Geir Dahl Strict Sign-Central Matrices . . . . . . 1202--1220
Vladimir Kazeev and
Christoph Schwab Tensor Approximation of Stationary
Distributions of Chemical Reaction
Networks . . . . . . . . . . . . . . . . 1221--1247
Daeshik Choi and
Anne Greenbaum An Algorithm for Finding a
$2$-Similarity Transformation from a
Numerical Contraction to a Contraction 1248--1262
Michele Benzi and
Valeria Simoncini Decay Bounds for Functions of Hermitian
Matrices with Banded or Kronecker
Structure . . . . . . . . . . . . . . . 1263--1282
Jianlin Xia and
Yuanzhe Xi and
Stephen Cauley and
Venkataramanan Balakrishnan Fast Sparse Selected Inversion . . . . . 1283--1314
Kim Batselier and
Haotian Liu and
Ngai Wong A Constructive Algorithm for Decomposing
a Tensor into a Finite Sum of
Orthonormal Rank-$1$ Terms . . . . . . . 1315--1337
Jennifer B. Erway and
Roummel F. Marcia On Efficiently Computing the Eigenvalues
of Limited-Memory Quasi-Newton Matrices 1338--1359
Dmitriy Drusvyatskiy and
Hon-Leung Lee and
Rekha R. Thomas Counting Real Critical Points of the
Distance to Orthogonally Invariant
Matrix Sets . . . . . . . . . . . . . . 1360--1380
Mikael Sòrensen and
Lieven De Lathauwer New Uniqueness Conditions for the
Canonical Polyadic Decomposition of
Third-Order Tensors . . . . . . . . . . 1381--1403
Nicolas Gillis and
Abhishek Kumar Exact and Heuristic Algorithms for
Semi-Nonnegative Matrix Factorization 1404--1424
Piers W. Lawrence and
Robert M. Corless Backward Error of Polynomial Eigenvalue
Problems Solved by Linearization of
Lagrange Interpolants . . . . . . . . . 1425--1442
Alexey Kuznetsov Explicit Hermite-type Eigenvectors of
the Discrete Fourier Transform . . . . . 1443--1464
F. Fogel and
R. Jenatton and
F. Bach and
A. d'Aspremont Convex Relaxations for Permutation
Problems . . . . . . . . . . . . . . . . 1465--1488
Xin-Guo Liu and
Xue-Feng Wang and
Wei-Guo Wang Maximization of Matrix Trace Function of
Product Stiefel Manifolds . . . . . . . 1489--1506
David F. Gleich and
Lek-Heng Lim and
Yongyang Yu Multilinear PageRank . . . . . . . . . . 1507--1541
Jiang Qian and
Delin Chu and
Roger C. E. Tan Analyticity of Semisimple Eigenvalues
and Corresponding Eigenvectors of
Matrix-Valued Functions . . . . . . . . 1542--1566
Ignat Domanov and
Lieven De Lathauwer Generic Uniqueness Conditions for the
Canonical Polyadic Decomposition and
INDSCAL . . . . . . . . . . . . . . . . 1567--1589
Anna Ma and
Deanna Needell and
Aaditya Ramdas Convergence Properties of the Randomized
Extended Gauss--Seidel and Kaczmarz
Methods . . . . . . . . . . . . . . . . 1590--1604
George S. Miminis Pole Placement in Single-Input Linear
Descriptor Systems . . . . . . . . . . . 1605--1621
D. A. Kolesnikov and
I. V. Oseledets From Low-Rank Approximation to a
Rational Krylov Subspace Method for the
Lyapunov Equation . . . . . . . . . . . 1622--1637
Cun Mu and
Daniel Hsu and
Donald Goldfarb Successive Rank-One Approximations for
Nearly Orthogonally Decomposable
Symmetric Tensors . . . . . . . . . . . 1638--1659
Robert M. Gower and
Peter Richtárik Randomized Iterative Methods for Linear
Systems . . . . . . . . . . . . . . . . 1660--1690
Yifan Sun and
Lieven Vandenberghe Decomposition Methods for Sparse Matrix
Nearness Problems . . . . . . . . . . . 1691--1717
J. J. P. Veerman and
David K. Hammond Tridiagonal Matrices and Boundary
Conditions . . . . . . . . . . . . . . . 1--17
Nicola Guglielmi and
Vladimir Yu. Protasov Invariant Polytopes of Sets of Matrices
with Application to Regularity of
Wavelets and Subdivisions . . . . . . . 18--52
Shreemayee Bora and
Ravi Srivastava Distance Problems for Hermitian Matrix
Pencils with Eigenvalues of Definite
Type . . . . . . . . . . . . . . . . . . 53--85
Elina Robeva Orthogonal Decomposition of Symmetric
Tensors . . . . . . . . . . . . . . . . 86--102
Yousef Saad Analysis of Subspace Iteration for
Eigenvalue Problems with Evolving
Matrices . . . . . . . . . . . . . . . . 103--122
Piers W. Lawrence and
Marc Van Barel and
Paul Van Dooren Backward Error Analysis of Polynomial
Eigenvalue Problems Solved by
Linearization . . . . . . . . . . . . . 123--144
Stefan Güttel and
Yuji Nakatsukasa Scaled and Squared Subdiagonal Padé
Approximation for the Matrix Exponential 145--170
Jinyan Fan and
Anwa Zhou The CP-Matrix Approximation Problem . . 171--194
Ding Lu and
Yangfeng Su and
Zhaojun Bai Stability Analysis of the Two-level
Orthogonal Arnoldi Procedure . . . . . . 195--214
Teng-Teng Yao and
Zheng-Jian Bai and
Zhi Zhao and
Wai-Ki Ching A Riemannian Fletcher--Reeves Conjugate
Gradient Method for Doubly Stochastic
Inverse Eigenvalue Problems . . . . . . 215--234
Yuanzhe Xi and
Ruipeng Li and
Yousef Saad An Algebraic Multilevel Preconditioner
with Low-Rank Corrections for Sparse
Symmetric Matrices . . . . . . . . . . . 235--259
Eliseu Fritscher and
Vilmar Trevisan Exploring Symmetries to Decompose
Matrices and Graphs Preserving the
Spectrum . . . . . . . . . . . . . . . . 260--289
Liping Chen and
Lixing Han and
Liangmin Zhou Computing Tensor Eigenvalues via
Homotopy Methods . . . . . . . . . . . . 290--319
Shmuel Friedland Remarks on the Symmetric Rank of
Symmetric Tensors . . . . . . . . . . . 320--337
K. Lessel and
M. Hartman and
S. Chandrasekaran A Fast Memory Efficient Construction
Algorithm for Hierarchically
Semi-Separable Representations . . . . . 338--353
Rafikul Alam and
Namita Behera Linearizations for Rational Matrix
Functions and Rosenbrock System
Polynomials . . . . . . . . . . . . . . 354--380
Bo Jiang and
Zhening Li and
Shuzhong Zhang Characterizing Real-Valued Multivariate
Complex Polynomials and Their Symmetric
Tensor Representations . . . . . . . . . 381--408
Shinji Ito and
Kazuo Murota An Algorithm for the Generalized
Eigenvalue Problem for Nonsquare Matrix
Pencils by Minimal Perturbation Approach 409--419
Michel Crouzeix Some Constants Related to Numerical
Ranges . . . . . . . . . . . . . . . . . 420--442
Francesca Arrigo and
Michele Benzi Edge Modification Criteria for Enhancing
the Communicability of Digraphs . . . . 443--468
Faisal Fairag and
Mohammed Alshahrani and
Hattan Tawfiq Bramble--Pasciak-Type Conjugate Gradient
Method for Darcy's Equations . . . . . . 469--489
Peter Benner and
Akwum Onwunta and
Martin Stoll Block-Diagonal Preconditioning for
Optimal Control Problems Constrained by
PDEs with Uncertain Inputs . . . . . . . 491--518
Antti Koskela and
Elias Jarlebring and
Michiel E. Hochstenbach Krylov Approximation of Linear ODEs with
Polynomial Parameterization . . . . . . 519--538
G. W. Stewart A Canonical CS Representation of a Pair
of Subspaces . . . . . . . . . . . . . . 539--549
Bo Dong and
Bo Yu and
Yan Yu A Homotopy Method for Finding All
Solutions of a Multiparameter Eigenvalue
Problem . . . . . . . . . . . . . . . . 550--571
P. E. Farrell The Number of Distinct Eigenvalues of a
Matrix After Perturbation . . . . . . . 572--576
Beresford Parlett and
Froilán M. Dopico and
Carla Ferreira The Inverse Eigenvector Problem for Real
Tridiagonal Matrices . . . . . . . . . . 577--597
Namgil Lee and
Andrzej Cichocki Regularized Computation of Approximate
Pseudoinverse of Large Matrices Using
Low-Rank Tensor Train Decompositions . . 598--623
Arash Massoudi and
Mark R. Opmeer and
Timo Reis Analysis of an Iteration Method for the
Algebraic Riccati Equation . . . . . . . 624--648
Yimin Wei and
Pengpeng Xie and
Liping Zhang Tikhonov Regularization and Randomized
GSVD . . . . . . . . . . . . . . . . . . 649--675
Victor Y. Pan How Bad Are Vandermonde Matrices? . . . 676--694
Petar Sirkovi\'c and
Daniel Kressner Subspace Acceleration for Large-Scale
Parameter-Dependent Hermitian
Eigenproblems . . . . . . . . . . . . . 695--718
João R. Cardoso and
Rui Ralha Matrix Arithmetic--Geometric Mean and
the Computation of the Logarithm . . . . 719--743
Laura Grigori and
Sophie Moufawad and
Frederic Nataf Enlarged Krylov Subspace Conjugate
Gradient Methods for Reducing
Communication . . . . . . . . . . . . . 744--773
Massimo Franchi and
Paolo Paruolo Inverting a Matrix Function around a
Singularity via Local Rank Factorization 774--797
Zhonggang Zeng Sensitivity and Computation of a
Defective Eigenvalue . . . . . . . . . . 798--817
Simon Etter and
Sergey Dolgov and
Boris N. Khoromskij Erratum: Two-Level QTT--Tucker Format
for Optimized Tensor Calculus . . . . . 818--822
Fernando De Terán and
Froilán M. Dopico Generic Change of the Partial
Multiplicities of Regular Matrix Pencils
under Low-Rank Perturbations . . . . . . 823--835
Francesca Arrigo and
Michele Benzi and
Caterina Fenu Computation of Generalized Matrix
Functions . . . . . . . . . . . . . . . 836--860
Iveta Hnetynková and
Martin Plesinger and
Diana Maria Sima Solvability of the Core Problem with
Multiple Right-Hand Sides in the TLS
Sense . . . . . . . . . . . . . . . . . 861--876
Hiroyuki Masuyama Error Bounds for Augmented Truncations
of Discrete-Time Block-Monotone Markov
Chains under Subgeometric Drift
Conditions . . . . . . . . . . . . . . . 877--910
Ching-Sung Liu and
Chun-Hua Guo and
Wen-Wei Lin A Positivity Preserving Inverse
Iteration for Finding the Perron Pair of
an Irreducible Nonnegative Third Order
Tensor . . . . . . . . . . . . . . . . . 911--932
Rushabh Patel and
Andrea Carron and
Francesco Bullo The Hitting Time of Multiple Random
Walks . . . . . . . . . . . . . . . . . 933--954
Klaus Neymeyr and
Ming Zhou Convergence Analysis of Restarted Krylov
Subspace Eigensolvers . . . . . . . . . 955--975
Yueh-Cheng Kuo and
Wen-Wei Lin and
Shih-Feng Shieh Structure-Preserving Flows of Symplectic
Matrix Pairs . . . . . . . . . . . . . . 976--1001
Peter Butkovic and
Daniel Jones On Special Cases of the Generalized
Max-Plus Eigenproblem . . . . . . . . . 1002--1021
Georgios Katsouleas and
John Maroulas An Inverse Problem for the $k$-Rank
Numerical Range . . . . . . . . . . . . 1022--1037
Andrei Draganescu and
Jyoti Saraswat Optimal-Order Preconditioners for Linear
Systems Arising in the Semismooth Newton
Solution of a Class of
Control-Constrained Problems . . . . . . 1038--1070
C. Greif and
C. C. Paige and
D. Titley-Peloquin and
J. M. Varah Numerical Equivalences among Krylov
Subspace Algorithms for Skew-Symmetric
Matrices . . . . . . . . . . . . . . . . 1071--1087
Nicholas J. Higham and
Natasa Strabi\'c Bounds for the Distance to the Nearest
Correlation Matrix . . . . . . . . . . . 1088--1102
Jennifer Pestana and
Tyrone Rees Null-Space Preconditioners for Saddle
Point Systems . . . . . . . . . . . . . 1103--1128
Amir Beck and
Shoham Sabach and
Marc Teboulle An Alternating Semiproximal Method for
Nonconvex Regularized Structured Total
Least Squares Problems . . . . . . . . . 1129--1150
B. Jeuris and
R. Vandebril The Kähler Mean of Block-Toeplitz
Matrices with Toeplitz Structured Blocks 1151--1175
Ke Ye and
Lek-Heng Lim Schubert Varieties and Distances between
Subspaces of Different Dimensions . . . 1176--1197
Ke Wei and
Jian-Feng Cai and
Tony F. Chan and
Shingyu Leung Guarantees of Riemannian Optimization
for Low Rank Matrix Recovery . . . . . . 1198--1222
Arvind K. Saibaba HOID: Higher Order Interpolatory
Decomposition for Tensors Based on
Tucker Representation . . . . . . . . . 1223--1249
Ning Zheng and
Ken Hayami and
Jun-Feng Yin Modulus-Type Inner Outer Iteration
Methods for Nonnegative Constrained
Least Squares Problems . . . . . . . . . 1250--1278
Yuanzhe Xi and
Jianlin Xia On the Stability of Some Hierarchical
Rank Structured Matrix Algorithms . . . 1279--1303
Kevin Carlberg and
Virginia Forstall and
Ray Tuminaro Krylov-Subspace Recycling via the
POD-Augmented Conjugate-Gradient Method 1304--1336
Anil Aswani Low-Rank Approximation and Completion of
Positive Tensors . . . . . . . . . . . . 1337--1364
Anne Greenbaum and
Trevor Caldwell and
Kenan Li Near Normal Dilations of Nonnormal
Matrices and Linear Operators . . . . . 1365--1381
Grey Ballard and
Austin R. Benson and
Alex Druinsky and
Benjamin Lipshitz and
Oded Schwartz Improving the Numerical Stability of
Fast Matrix Multiplication . . . . . . . 1382--1418
Yvan Notay Algebraic Two-Level Convergence Theory
for Singular Systems . . . . . . . . . . 1419--1439
Zhening Li Bounds on the Spectral Norm and the
Nuclear Norm of a Tensor Based on Tensor
Partitions . . . . . . . . . . . . . . . 1440--1452
Mary Aprahamian and
Nicholas J. Higham Matrix Inverse Trigonometric and Inverse
Hyperbolic Functions: Theory and
Algorithms . . . . . . . . . . . . . . . 1453--1477
Fredy Sosa and
Julio Moro First Order Asymptotic Expansions for
Eigenvalues of Multiplicatively
Perturbed Matrices . . . . . . . . . . . 1478--1504
Michael Stewart On the Description and Stability of
Orthogonal Transformations of Rank
Structured Matrices . . . . . . . . . . 1505--1530
Berkant Savas and
Inderjit S. Dhillon Clustered Matrix Approximation . . . . . 1531--1555
Yang Qi and
Pierre Comon and
Lek-Heng Lim Semialgebraic Geometry of Nonnegative
Tensor Rank . . . . . . . . . . . . . . 1556--1580
Jiang Qian and
Delin Chu and
Roger C. E. Tan A Systematic Analysis on Analyticity of
Semisimple Eigenvalues of Matrix-Valued
Functions . . . . . . . . . . . . . . . 1581--1599
Vanni Noferini and
Javier Pérez Fiedler-comrade and Fiedler--Chebyshev
pencils . . . . . . . . . . . . . . . . 1600--1624
Christian Mehl and
Volker Mehrmann and
Punit Sharma Stability Radii for Linear Hamiltonian
Systems with Dissipation Under
Structure-Preserving Perturbations . . . 1625--1654
V. Simoncini Analysis of the Rational Krylov Subspace
Projection Method for Large-Scale
Algebraic Riccati Equations . . . . . . 1655--1674
Ziyan Luo and
Liqun Qi Completely Positive Tensors: Properties,
Easily Checkable Subclasses, and
Tractable Relaxations . . . . . . . . . 1675--1698
M. A. Iwen and
B. W. Ong A Distributed and Incremental SVD
Algorithm for Agglomerative Data
Analysis on Large Networks . . . . . . . 1699--1718
Xinzhen Zhang and
Zheng-Hai Huang and
Liqun Qi Comon's Conjecture, Rank Decomposition,
and Symmetric Rank Decomposition of
Symmetric Tensors . . . . . . . . . . . 1719--1728
Michael Stewart Rank Decisions in Matrix Quotient
Decompositions . . . . . . . . . . . . . 1729--1746
Shenglong Hu and
Liqun Qi A Necessary and Sufficient Condition for
Existence of a Positive Perron Vector 1747--1770
Yuji Nakatsukasa and
Vanni Noferini and
Alex Townsend Vector Spaces of Linearizations for
Matrix Polynomials: a Bivariate
Polynomial Approach . . . . . . . . . . 1--29
Peizhen Zhu and
Andrew V. Knyazev Rayleigh--Ritz Majorization Error Bounds
of Mixed Type . . . . . . . . . . . . . 30--49
Yunfeng Cai and
Chengyu Liu An Algebraic Approach to Nonorthogonal
General Joint Block Diagonalization . . 50--71
C. Mehl and
V. Mehrmann and
M. Wojtylak Parameter-Dependent Rank-One
Perturbations of Singular Hermitian Or
Symmetric Pencils . . . . . . . . . . . 72--95
Gérard Meurant The Coefficients of the FOM and GMRES
Residual Polynomials . . . . . . . . . . 96--117
Gang Wu The Convergence of Harmonic Ritz Vectors
and Harmonic Ritz Values, Revisited . . 118--133
Hannes Gernandt and
Carsten Trunk Eigenvalue Placement for Regular Matrix
Pencils with Rank One Perturbations . . 134--154
Hao Wang and
Qiang Ye Error Bounds for the Krylov Subspace
Methods for Computations of Matrix
Exponentials . . . . . . . . . . . . . . 155--187
Leonardo Robol and
Raf Vandebril and
Paul Van Dooren A Framework for Structured
Linearizations of Matrix Polynomials in
Various Bases . . . . . . . . . . . . . 188--216
Patrick E. Farrell and
John W. Pearson A Preconditioner for the Ohta--Kawasaki
Equation . . . . . . . . . . . . . . . . 217--225
Gregoire Pichon and
Mathieu Faverge and
Pierre Ramet and
Jean Roman Reordering Strategy for Blocking
Optimization in Sparse Linear Solvers 226--248
María I. Bueno and
Froilán M. Dopico and
Susana Furtado Linearizations of Hermitian Matrix
Polynomials Preserving the Sign
Characteristic . . . . . . . . . . . . . 249--272
Zaiwen Wen and
Yin Zhang Accelerating Convergence by Augmented
Rayleigh--Ritz Projections For
Large-Scale Eigenpair Computation . . . 273--296
Ian N. Zwaan and
Michiel E. Hochstenbach Krylov--Schur-Type Restarts for the
Two-Sided Arnoldi Method . . . . . . . . 297--321
Ralf Zimmermann A Matrix-Algebraic Algorithm for the
Riemannian Logarithm on the Stiefel
Manifold under the Canonical Metric . . 322--342
Caterina Fenu and
Desmond J. Higham Block Matrix Formulations for Evolving
Networks . . . . . . . . . . . . . . . . 343--360
Nicola Guglielmi and
Mutti-Ur Rehman and
Daniel Kressner A Novel Iterative Method To Approximate
Structured Singular Values . . . . . . . 361--386
Teng Zhang A Majorization-Minimization Algorithm
for Computing the Karcher Mean of
Positive Definite Matrices . . . . . . . 387--400
Mian Ilyas Ahmad and
Daniel B. Szyld and
Martin B. van Gijzen Preconditioned Multishift BiCG for $
\mathcal {H}_2 $-Optimal Model Reduction 401--424
Arthur Szlam and
Andrew Tulloch and
Mark Tygert Accurate Low-Rank Approximations Via a
Few Iterations of Alternating Least
Squares . . . . . . . . . . . . . . . . 425--433
Vanni Noferini A Formula for the Fréchet Derivative of a
Generalized Matrix Function . . . . . . 434--457
Julianne Chung and
Matthias Chung Optimal Regularized Inverse Matrices for
Inverse Problems . . . . . . . . . . . . 458--477
Nguyen Thanh Son and
Tatjana Stykel Solving Parameter-Dependent Lyapunov
Equations Using the Reduced Basis Method
with Application to Parametric Model
Order Reduction . . . . . . . . . . . . 478--504
Michael T. Schaub and
Maguy Trefois and
Paul van Dooren and
Jean-Charles Delvenne Sparse Matrix Factorizations for Fast
Linear Solvers with Application to
Laplacian Systems . . . . . . . . . . . 505--529
Aritra Dutta and
Xin Li On a Problem of Weighted Low-Rank
Approximation of Matrices . . . . . . . 530--553
Phillip Ainsleigh A Method for Computing Moments of
Quadratic Forms Involving Wrapped Random
Variables . . . . . . . . . . . . . . . 554--573
L. Gemignani and
L. Robol Fast Hessenberg Reduction of Some Rank
Structured Matrices . . . . . . . . . . 574--598
Wim Michiels and
Islam Boussaada and
Silviu-Iulian Niculescu An Explicit Formula for the Splitting of
Multiple Eigenvalues for Nonlinear
Eigenvalue Problems and Connections with
the Linearization for the Delay
Eigenvalue Problem . . . . . . . . . . . 599--620
Colin Ponce and
Panayot S. Vassilevski Solving Graph Laplacian Systems Through
Recursive Partitioning and Two-Grid
Preconditioning . . . . . . . . . . . . 621--648
M. Crouzeix and
C. Palencia The Numerical Range is a $ (1 + \sqrt
{2}) $-Spectral Set . . . . . . . . . . 649--655
Luca Chiantini and
Giorgio Ottaviani and
Nick Vannieuwenhoven Effective Criteria for Specific
Identifiability of Tensors and Forms . . 656--681
Piers W. Lawrence and
Javier Pérez Constructing Strong Linearizations of
Matrix Polynomials Expressed in
Chebyshev Bases . . . . . . . . . . . . 683--709
Andreas Frommer and
Kathryn Lund and
Marcel Schweitzer and
Daniel B. Szyld The Radau--Lanczos Method for Matrix
Functions . . . . . . . . . . . . . . . 710--732
A. Bostan and
C.-P. Jeannerod and
C. Mouilleron and
É. Schost On Matrices With Displacement Structure:
Generalized Operators and Faster
Algorithms . . . . . . . . . . . . . . . 733--775
Nicola Guglielmi and
Christian Lubich and
Volker Mehrmann On the Nearest Singular Matrix Pencil 776--806
Ruipeng Li and
Yousef Saad Low-Rank Correction Methods for
Algebraic Domain Decomposition
Preconditioners . . . . . . . . . . . . 807--828
Adolfo R. Escobedo and
Erick Moreno-Centeno Roundoff-Error-Free Basis Updates of $ L
U $ Factorizations for the Efficient
Validation of Optimality Certificates 829--853
Pengwen Chen and
Albert Fannjiang and
Gi-Ren Liu Phase Retrieval by Linear Algebra . . . 854--868
Minghua Chen and
Weihua Deng Convergence Analysis of a Multigrid
Method for a Nonlocal Model . . . . . . 869--890
Ding Lu and
Bart Vandereycken Criss-Cross Type Algorithms for
Computing the Real Pseudospectral
Abscissa . . . . . . . . . . . . . . . . 891--923
Bing Zheng and
Lingsheng Meng and
Yimin Wei Condition Numbers of the
Multidimensional Total Least Squares
Problem . . . . . . . . . . . . . . . . 924--948
Nicola Mastronardi and
Paul Van Dooren Computing the Jordan Structure of an
Eigenvalue . . . . . . . . . . . . . . . 949--966
Erna Begovi\'c Kovac and
Daniel Kressner Structure-Preserving Low Multilinear
Rank Approximation of Antisymmetric
Tensors . . . . . . . . . . . . . . . . 967--983
Daniel Kressner and
Ana Susnjara Fast Computation of Spectral Projectors
of Banded Matrices . . . . . . . . . . . 984--1009
Steven P. Diaz and
Adam Lutoborski Discrete Fourier Transform Tensors and
Their Ranks . . . . . . . . . . . . . . 1010--1027
Mark Embree and
Blake Keeler Pseudospectra of Matrix Pencils for
Transient Analysis of
Differential-Algebraic Equations . . . . 1028--1054
Martin Paton and
Kerem Akartunali and
Desmond J. Higham Centrality Analysis for Modified
Lattices . . . . . . . . . . . . . . . . 1055--1073
Shashanka Ubaru and
Jie Chen and
Yousef Saad Fast Estimation of $ {\rm tr}(f(A)) $
via Stochastic Lanczos Quadrature . . . 1075--1099
Stanley C. Eisenstat and
Serge Gratton and
David Titley-Peloquin On the Symmetric Componentwise Relative
Backward Error for Linear Systems of
Equations . . . . . . . . . . . . . . . 1100--1115
Haim Avron and
Kenneth L. Clarkson and
David P. Woodruff Faster Kernel Ridge Regression Using
Sketching and Preconditioning . . . . . 1116--1138
Darshan Bryner Endpoint Geodesics on the Stiefel
Manifold Embedded in Euclidean Space . . 1139--1159
James Hook and
Françoise Tisseur Incomplete $ L U $ Preconditioner Based
on Max-Plus Approximation of $ L U $
Factorization . . . . . . . . . . . . . 1160--1189
Jiang Qian and
Yunfeng Cai and
Delin Chu and
Roger C. E. Tan Eigenvalue Embedding of Undamped
Vibroacoustic Systems with No-spillover 1190--1209
Cun Mu and
Daniel Hsu and
Donald Goldfarb Greedy Approaches to Symmetric
Orthogonal Tensor Decomposition . . . . 1210--1226
Bernhard Beckermann and
Alex Townsend On the Singular Values of Matrices with
Displacement Structure . . . . . . . . . 1227--1248
Andrii Dmytryshyn and
Stefan Johansson and
Bo Kågström Canonical Structure Transitions of
System Pencils . . . . . . . . . . . . . 1249--1267
Xin Ye and
Jianlin Xia and
Raymond H. Chan and
Stephen Cauley and
Venkataramanan Balakrishnan A Fast Contour-Integral Eigensolver for
Non-Hermitian Matrices . . . . . . . . . 1268--1297
Jianlin Xia and
Zixing Xin Effective and Robust Preconditioning of
General SPD Matrices via Structured
Incomplete Factorization . . . . . . . . 1298--1322
N. Guglielmi and
M. Gürbüzbalaban and
T. Mitchell and
M. L. Overton Approximating the Real Structured
Stability Radius with Frobenius-Norm
Bounded Perturbations . . . . . . . . . 1323--1353
Evan S. Gawlik and
Melvin Leok Iterative Computation of the Fréchet
Derivative of the Polar Decomposition 1354--1379
Robert M. Gower and
Peter Richtárik Randomized Quasi-Newton Updates Are
Linearly Convergent Matrix Inversion
Algorithms . . . . . . . . . . . . . . . 1380--1409
James Hook Max-Plus Algebraic Statistical Leverage
Scores . . . . . . . . . . . . . . . . . 1410--1433
Ignat Domanov and
Alwin Stegeman and
Lieven De Lathauwer On the Largest Multilinear Singular
Values of Higher-Order Tensors . . . . . 1434--1453
Joel A. Tropp and
Alp Yurtsever and
Madeleine Udell and
Volkan Cevher Practical Sketching Algorithms for
Low-Rank Matrix Approximation . . . . . 1454--1485
Daniel Loghin A Note on Constraint Preconditioning . . 1486--1495
Nicat Aliyev and
Peter Benner and
Emre Mengi and
Paul Schwerdtner and
Matthias Voigt Large-Scale Computation of $ \mathcal
{L}_\infty $-Norms by a Greedy Subspace
Method . . . . . . . . . . . . . . . . . 1496--1516
Jiawang Nie Low Rank Symmetric Tensor Approximations 1517--1540
P. Donelan and
J. M. Selig Hyperbolic Pseudoinverses for Kinematics
in the Euclidean Group . . . . . . . . . 1541--1559
George A. Hagedorn and
Caroline Lasser Symmetric Kronecker Products and
Semiclassical Wave Packets . . . . . . . 1560--1579
Xue-lei Lin and
Michael K. Ng and
Hai-Wei Sun A Splitting Preconditioner for
Toeplitz-Like Linear Systems Arising
from Fractional Diffusion Equations . . 1580--1614
Jianze Li and
Konstantin Usevich and
Pierre Comon Globally Convergent Jacobi-Type
Algorithms for Simultaneous Orthogonal
Symmetric Tensor Diagonalization . . . . 1--22
Daniel Kressner and
Robert Luce Fast Computation of the Matrix
Exponential for a Toeplitz Matrix . . . 23--47
Fatih Kangal and
Karl Meerbergen and
Emre Mengi and
Wim Michiels A Subspace Method for Large-Scale
Eigenvalue Optimization . . . . . . . . 48--82
Balázs Gerencsér and
Vladimir V. Gusev and
Raphaël M. Jungers Primitive Sets of Nonnegative Matrices
and Synchronizing Automata . . . . . . . 83--98
Simon Foucart Concave Mirsky Inequality and Low-Rank
Recovery . . . . . . . . . . . . . . . . 99--103
Anna Ma and
Deanna Needell and
Aaditya Ramdas Iterative Methods for Solving Factorized
Linear Systems . . . . . . . . . . . . . 104--122
Andrea Franceschini and
Victor Antonio Paludetto Magri and
Massimiliano Ferronato and
Carlo Janna A Robust Multilevel Approximate Inverse
Preconditioner for Symmetric Positive
Definite Matrices . . . . . . . . . . . 123--147
Yuji Nakatsukasa and
Leo Taslaman and
Françoise Tisseur and
Ion Zaballa Reduction of Matrix Polynomials to
Simpler Forms . . . . . . . . . . . . . 148--177
Massimiliano Fasi and
Bruno Iannazzo Computing the Weighted Geometric Mean of
Two Large-Scale Matrices and Its Inverse
Times a Vector . . . . . . . . . . . . . 178--203
Vu Hoang Linh and
Ngo Thi Thanh Nga and
Do Duc Thuan Exponential Stability and Robust
Stability for Linear Time-Varying
Singular Systems of Second Order
Difference Equations . . . . . . . . . . 204--233
Ralf Zimmermann and
Benjamin Peherstorfer and
Karen Willcox Geometric Subspace Updates with
Applications to Online Adaptive
Nonlinear Model Reduction . . . . . . . 234--261
Luis García Ramos and
Reinhard Nabben On the Spectrum of Deflated Matrices
with Applications to the Deflated
Shifted Laplace Preconditioner for the
Helmholtz Equation . . . . . . . . . . . 262--286
Paul Breiding and
Nick Vannieuwenhoven The Condition Number of Join
Decompositions . . . . . . . . . . . . . 287--309
Peter Grindrod and
Desmond J. Higham and
Vanni Noferini The Deformed Graph Laplacian and Its
Applications to Network Centrality
Analysis . . . . . . . . . . . . . . . . 310--341
Thomas Ransford and
Felix L. Schwenninger Remarks on the Crouzeix--Palencia Proof
that the Numerical Range is a $ (1 +
\sqrt 2)$-Spectral Set . . . . . . . . . 342--345
Christer Glader and
Mikael Kurula and
Mikael Lindström Crouzeix's Conjecture Holds for
Tridiagonal $ 3 \times 3 $ Matrices with
Elliptic Numerical Range Centered at an
Eigenvalue . . . . . . . . . . . . . . . 346--364
Michael Stewart Numerical Rank Deficiency in Matrix
Products . . . . . . . . . . . . . . . . 365--399
Zhening Li and
Yuji Nakatsukasa and
Tasuku Soma and
André Uschmajew On Orthogonal Tensors and Best Rank-One
Approximation Ratio . . . . . . . . . . 400--425
Siegfried Cools and
Emrullah Fatih Yetkin and
Emmanuel Agullo and
Luc Giraud and
Wim Vanroose Analyzing the Effect of Local Rounding
Error Propagation on the Maximal
Attainable Accuracy of the Pipelined
Conjugate Gradient Method . . . . . . . 426--450
Valentin Khrulkov and
Ivan Oseledets Desingularization of Bounded-Rank Matrix
Sets . . . . . . . . . . . . . . . . . . 451--471
Massimiliano Fasi and
Nicholas J. Higham Multiprecision Algorithms for Computing
the Matrix Logarithm . . . . . . . . . . 472--491
Howard C. Elman and
Tengfei Su A Low-Rank Multigrid Method for the
Stochastic Steady-State Diffusion
Problem . . . . . . . . . . . . . . . . 492--509
Florian Feppon and
Pierre F. J. Lermusiaux A Geometric Approach to Dynamical Model
Order Reduction . . . . . . . . . . . . 510--538
Bernhard Beckermann and
Daniel Kressner and
Marcel Schweitzer Low-Rank Updates of Matrix Functions . . 539--565
Petros Drineas and
Ilse C. F. Ipsen and
Eugenia-Maria Kontopoulou and
Malik Magdon-Ismail Structural Convergence Results for
Approximation of Dominant Subspaces from
Block Krylov Spaces . . . . . . . . . . 567--586
Rafikul Alam and
Namita Behera Generalized Fiedler Pencils for Rational
Matrix Functions . . . . . . . . . . . . 587--610
Lei-Hong Zhang and
Chungen Shen and
Wei Hong Yang and
Joaquim J. Júdice A Lanczos Method for Large-Scale Extreme
Lorentz Eigenvalue Problems . . . . . . 611--631
Mehdi S. Mousavi and
Hristo S. Sendov A Unified Approach to Spectral and
Isotropic Functions . . . . . . . . . . 632--663
Sirani M. Perera and
Jianhua Liu Lowest Complexity Self-Recursive Radix-2
DCT II/III Algorithms . . . . . . . . . 664--682
Meiyue Shao and
Felipe H. da Jornada and
Lin Lin and
Chao Yang and
Jack Deslippe and
Steven G. Louie A Structure Preserving Lanczos Algorithm
for Computing the Optical Absorption
Spectrum . . . . . . . . . . . . . . . . 683--711
Daniel Ruiz and
Annick Sartenaer and
Charlotte Tannier Refining the Lower Bound on the Positive
Eigenvalues of Saddle Point Matrices
with Insights on the Interactions
between the Blocks . . . . . . . . . . . 712--736
Bernhard Beckermann and
Clara Mertens and
Raf Vandebril On an Economic Arnoldi Method for $ B M
L $-Matrices . . . . . . . . . . . . . . 737--768
Trevor Caldwell and
Anne Greenbaum and
Kenan Li Some Extensions of the
Crouzeix--Palencia Result . . . . . . . 769--780
Jeffrey Uhlmann A Generalized Matrix Inverse That Is
Consistent with Respect to Diagonal
Transformations . . . . . . . . . . . . 781--800
Evan S. Gawlik and
Melvin Leok High-Order Retractions on Matrix
Manifolds Using Projected Polynomials 801--828
Xin Xing and
Edmond Chow Preserving Positive Definiteness in
Hierarchically Semiseparable Matrix
Approximations . . . . . . . . . . . . . 829--855
Junjun Pan and
Michael K. Ng Orthogonal Nonnegative Matrix
Factorization by Sparsity and Nuclear
Norm Optimization . . . . . . . . . . . 856--875
Casey Battaglino and
Grey Ballard and
Tamara G. Kolda A Practical Randomized CP Tensor
Decomposition . . . . . . . . . . . . . 876--901
Fatemeh Panjeh Ali Beik and
Michele Benzi Iterative Methods for Double Saddle
Point Systems . . . . . . . . . . . . . 902--921
Serge Gratton and
David Titley-Peloquin Improved Bounds for Small-Sample
Estimation . . . . . . . . . . . . . . . 922--931
Daniel Drzisga and
Lorenz John and
Ulrich Rüde and
Barbara Wohlmuth and
Walter Zulehner On the Analysis of Block Smoothers for
Saddle Point Problems . . . . . . . . . 932--960
Daniel Kressner and
Ding Lu and
Bart Vandereycken Subspace Acceleration for the Crawford
Number and Related Eigenvalue
Optimization Problems . . . . . . . . . 961--982
Peter Benner and
Pawan Goyal and
Serkan Gugercin $ \mathcal H_2 $-Quasi-Optimal Model
Order Reduction for Quadratic-Bilinear
Control Systems . . . . . . . . . . . . 983--1032
Keiichi Morikuni and
Miroslav Rozlozník On GMRES for Singular EP and GP Systems 1033--1048
Klaus Neymeyr and
Mathias Sawall On the Set of Solutions of the
Nonnegative Matrix Factorization Problem 1049--1069
Ariel Jaffe and
Roi Weiss and
Boaz Nadler Newton Correction Methods for Computing
Real Eigenpairs of Symmetric Tensors . . 1071--1094
Yu Guan and
Moody T. Chu and
Delin Chu SVD-Based Algorithms for the Best Rank-1
Approximation of a Symmetric Tensor . . 1095--1115
Fernando De Terán A Geometric Description of the Sets of
Palindromic and Alternating Matrix
Pencils with Bounded Rank . . . . . . . 1116--1134
Satoru Iwata and
Mizuyo Takamatsu Index Reduction via Unimodular
Transformations . . . . . . . . . . . . 1135--1151
Zlatko Drmac and
Arvind Krishna Saibaba The Discrete Empirical Interpolation
Method: Canonical Structure and
Formulation in Weighted Inner Product
Spaces . . . . . . . . . . . . . . . . . 1152--1180
Jiang Hu and
Andre Milzarek and
Zaiwen Wen and
Yaxiang Yuan Adaptive Quadratically Regularized
Newton Method for Riemannian
Optimization . . . . . . . . . . . . . . 1181--1207
John T. Holodnak and
Ilse C. F. Ipsen and
Ralph C. Smith A Probabilistic Subspace Bound with
Application to Active Subspaces . . . . 1208--1220
Kim Batselier and
Wenjian Yu and
Luca Daniel and
Ngai Wong Computing Low-Rank Approximations of
Large-Scale Matrices with the Tensor
Network Randomized SVD . . . . . . . . . 1221--1244
Jared L. Aurentz and
Thomas Mach and
Leonardo Robol and
Raf Vandebril and
David S. Watkins Fast and Backward Stable Computation of
Roots of Polynomials, Part II: Backward
Error Analysis; Companion Matrix and
Companion Pencil . . . . . . . . . . . . 1245--1269
Zvonimir Bujanovi\'c and
Lars Karlsson and
Daniel Kressner A Householder-Based Algorithm for
Hessenberg-Triangular Reduction . . . . 1270--1294
Eric Hallman and
Ming Gu LSMB: Minimizing the Backward Error for
Least-Squares Problems . . . . . . . . . 1295--1317
Erin C. Carson The Adaptive $s$-Step Conjugate Gradient
Method . . . . . . . . . . . . . . . . . 1318--1338
Wenjian Yu and
Yu Gu and
Yaohang Li Efficient Randomized Algorithms for the
Fixed-Precision Low-Rank Matrix
Approximation . . . . . . . . . . . . . 1339--1359
Yunfeng Cai and
Lei-Hong Zhang and
Zhaojun Bai and
Ren-Cang Li On an Eigenvector-Dependent Nonlinear
Eigenvalue Problem . . . . . . . . . . . 1360--1382
Pietro Benedusi and
Carlo Garoni and
Rolf Krause and
Xiaozhou Li and
Stefano Serra-Capizzano Space--Time FE--DG Discretization of the
Anisotropic Diffusion Equation in Any
Dimension: The Spectral Symbol . . . . . 1383--1420
Simon Telen and
Bernard Mourrain and
Marc Van Barel Solving Polynomial Systems via Truncated
Normal Forms . . . . . . . . . . . . . . 1421--1447
Evan S. Gawlik and
Yuji Nakatsukasa and
Brian D. Sutton A Backward Stable Algorithm for
Computing the CS Decomposition via the
Polar Decomposition . . . . . . . . . . 1448--1469
Fredrik Andersson and
Marcus Carlsson ESPRIT for Multidimensional General
Grids . . . . . . . . . . . . . . . . . 1470--1488
C. Mehl and
V. Mehrmann and
M. Wojtylak Linear Algebra Properties of Dissipative
Hamiltonian Descriptor Systems . . . . . 1489--1519
Stefano Pozza and
Francesco Tudisco On the Stability of Network Indices
Defined by Means of Matrix Functions . . 1521--1546
Weiwei Xu and
Hong-Kui Pang and
Wen Li and
Xueping Huang and
Wenjie Guo On the Explicit Expression of Chordal
Metric between Generalized Singular
Values of Grassmann Matrix Pairs with
Applications . . . . . . . . . . . . . . 1547--1563
Stefano Massei and
Davide Palitta and
Leonardo Robol Solving Rank-Structured Sylvester and
Lyapunov Equations . . . . . . . . . . . 1564--1590
Nicola Mastronardi and
Paul Van Dooren The $ Q R $ Steps with Perfect Shifts 1591--1615
Yuehua Feng and
Jianwei Xiao and
Ming Gu Randomized Complete Pivoting for Solving
Symmetric Indefinite Linear Systems . . 1616--1641
Nicola Guglielmi and
Vladimir Yu. Protasov On the Closest Stable/Unstable
Nonnegative Matrix and Related Stability
Radii . . . . . . . . . . . . . . . . . 1642--1669
A. Amparan and
F. M. Dopico and
S. Marcaida and
I. Zaballa Strong Linearizations of Rational
Matrices . . . . . . . . . . . . . . . . 1670--1700
Emmanuel Agullo and
Eric Darve and
Luc Giraud and
Yuval Harness Low-Rank Factorizations in Data Sparse
Hierarchical Algorithms for
Preconditioning Symmetric Positive
Definite Matrices . . . . . . . . . . . 1701--1725
Sébastien Loisel and
Peter Maxwell Path-Following Method to Determine the
Field of Values of a Matrix with High
Accuracy . . . . . . . . . . . . . . . . 1726--1749
Arnab Ghosh and
Rafikul Alam Sensitivity and Backward Perturbation
Analysis of Multiparameter Eigenvalue
Problems . . . . . . . . . . . . . . . . 1750--1775
Emre Mengi Large-Scale and Global Maximization of
the Distance to Instability . . . . . . 1776--1809
Ruoxi Wang and
Yingzhou Li and
Eric Darve On the Numerical Rank of Radial Basis
Function Kernels in High Dimensions . . 1810--1835
Clarissa Garvey and
Chang Meng and
James G. Nagy Singular Value Decomposition
Approximation via Kronecker Summations
for Imaging Applications . . . . . . . . 1836--1857
Eleonora Andreotti and
Dominik Edelmann and
Nicola Guglielmi and
Christian Lubich Constrained Graph Partitioning via
Matrix Differential Equations . . . . . 1--22
Arvind K. Saibaba Randomized Subspace Iteration: Analysis
of Canonical Angles and Unitarily
Invariant Norms . . . . . . . . . . . . 23--48
Katherine Fitch Effective Resistance Preserving Directed
Graph Symmetrization . . . . . . . . . . 49--65
Hussam Al Daas and
Laura Grigori A Class of Efficient Locally Constructed
Preconditioners Based on Coarse Spaces 66--91
Ivan Dokmani\'c and
Rémi Gribonval Concentration of the Frobenius Norm of
Generalized Matrix Inverses . . . . . . 92--121
Yvan Notay Convergence of Some Iterative Methods
for Symmetric Saddle Point Linear
Systems . . . . . . . . . . . . . . . . 122--146
Jürgen Dölz and
Helmut Harbrecht and
Michael D. Multerer On the Best Approximation of the
Hierarchical Matrix Product . . . . . . 147--174
Diego Armentano and
Carlos Beltrán The Polynomial Eigenvalue Problem is
Well Conditioned for Random Inputs . . . 175--193
Mustafa Ç. Pinar Necessary and Sufficient Conditions for
Noiseless Sparse Recovery via Convex
Quadratic Splines . . . . . . . . . . . 194--209
Jared L. Aurentz and
Anthony P. Austin and
Michele Benzi and
Vassilis Kalantzis Stable Computation of Generalized Matrix
Functions via Polynomial Interpolation 210--234
Ron Estrin and
Dominique Orban and
Michael Saunders Euclidean-Norm Error Bounds for SYMMLQ
and CG . . . . . . . . . . . . . . . . . 235--253
Ron Estrin and
Dominique Orban and
Michael A. Saunders LSLQ: an Iterative Method for Linear
Least-Squares with an Error Minimization
Property . . . . . . . . . . . . . . . . 254--275
Parsiad Azimzadeh and
Erhan Bayraktar High Order Bellman Equations and Weakly
Chained Diagonally Dominant Tensors . . 276--298
Petros Drineas and
Ilse C. F. Ipsen Low-Rank Matrix Approximations Do Not
Need a Singular Value Gap . . . . . . . 299--319
James Hook and
Jennifer Pestana and
Françoise Tisseur and
Jonathan Hogg Max-Balanced Hungarian Scalings . . . . 320--346
Marija Dodig and
Marko Stosi\'c The General Matrix Pencil Completion
Problem: a Minimal Case . . . . . . . . 347--369
Lek-Heng Lim and
Ken Sze-Wai Wong and
Ke Ye Numerical Algorithms on the Affine
Grassmannian . . . . . . . . . . . . . . 371--393
Max Pfeffer and
Anna Seigal and
Bernd Sturmfels Learning Paths from Signature Tensors 394--416
Emmanuel Agullo and
Luc Giraud and
Louis Poirel Robust Preconditioners via Generalized
Eigenproblems for Hybrid Sparse Linear
Solvers . . . . . . . . . . . . . . . . 417--439
Itziar Baragaña and
Alicia Roca Weierstrass Structure and Eigenvalue
Placement of Regular Matrix Pencils
under Low Rank Perturbations . . . . . . 440--453
Liron Mor-Yosef and
Haim Avron Sketching for Principal Component
Regression . . . . . . . . . . . . . . . 454--485
Jiawang Nie and
Ke Ye Hankel Tensor Decompositions and Ranks 486--516
Sabine Le Borne Factorization, Symmetrization, and
Truncated Transformation of Radial Basis
Function-GA Stabilized Gaussian Radial
Basis Functions . . . . . . . . . . . . 517--541
Giulia Sacchi and
Valeria Simoncini A GMRES Convergence Analysis for
Localized Invariant Subspace
Ill-Conditioning . . . . . . . . . . . . 542--563
Ben S. Southworth Necessary Conditions and Tight Two-level
Convergence Bounds for Parareal and
Multigrid Reduction in Time . . . . . . 564--608
Christopher Lourenco and
Adolfo R. Escobedo and
Erick Moreno-Centeno and
Timothy A. Davis Exact Solution of Sparse Linear Systems
via Left-Looking Roundoff-Error-Free $ L
U $ Factorization in Time Proportional
to Arithmetic Work . . . . . . . . . . . 609--638
Gabriel Oksa and
Yusaku Yamamoto and
Martin Becka and
Marián Vajtersic Asymptotic Quadratic Convergence of the
Two-Sided Serial and Parallel
Block-Jacobi SVD Algorithm . . . . . . . 639--671
Rafikul Alam and
Sk. Safique Ahmad Sensitivity Analysis of Nonlinear
Eigenproblems . . . . . . . . . . . . . 672--695
Evan S. Gawlik Zolotarev Iterations for the Matrix
Square Root . . . . . . . . . . . . . . 696--719
Luis M. Anguas and
Froilán M. Dopico and
Richard Hollister and
D. Steven Mackey Van Dooren's Index Sum Theorem and
Rational Matrices with Prescribed
Structural Data . . . . . . . . . . . . 720--738
Carlos Beltrán and
Paul Breiding and
Nick Vannieuwenhoven Pencil-Based Algorithms for Tensor Rank
Decomposition are not Stable . . . . . . 739--773
Bahar Arslan and
Vanni Noferini and
Françoise Tisseur The Structured Condition Number of a
Differentiable Map between Matrix
Manifolds, with Applications . . . . . . 774--799
I. Ben Gharbia and
J. Ch. Gilbert An Algorithmic Characterization of
P-matricity II: Adjustments,
Refinements, and Validation . . . . . . 800--813
Florian Feppon and
Pierre F. J. Lermusiaux The Extrinsic Geometry of Dynamical
Systems Tracking Nonlinear Matrix
Projections . . . . . . . . . . . . . . 814--844
Wim Michiels and
Bin Zhou Computing Delay Lyapunov Matrices and $
\mathcal {H}_2 $ Norms for Large-scale
Problems . . . . . . . . . . . . . . . . 845--869
J. Pestana Preconditioners for Symmetrized Toeplitz
and Multilevel Toeplitz Matrices . . . . 870--887
Mikael Sòrensen and
Lieven De Lathauwer Fiber Sampling Approach to Canonical
Polyadic Decomposition and Application
to Tensor Completion . . . . . . . . . . 888--917
Zhonggang Zeng On the Sensitivity of Singular and
Ill-Conditioned Linear Systems . . . . . 918--942
Daan Camps and
Karl Meerbergen and
Raf Vandebril A Rational $ Q Z $ Method . . . . . . . 943--972
Roy Mitz and
Nir Sharon and
Yoel Shkolnisky Symmetric Rank-One Updates from Partial
Spectrum with an Application to
Out-of-Sample Extension . . . . . . . . 973--997
Dana Lahat and
Christian Jutten and
Helene Shapiro Schur's Lemma for Coupled Reducibility
and Coupled Normality . . . . . . . . . 998--1021
Michiel E. Hochstenbach and
Christian Mehl and
Bor Plestenjak Solving Singular Generalized Eigenvalue
Problems by a Rank-Completing
Perturbation . . . . . . . . . . . . . . 1022--1046
Yu Guan and
Delin Chu Numerical Computation for Orthogonal
Low-Rank Approximation of Tensors . . . 1047--1065
Paola Ferrari and
Isabella Furci and
Sean Hon and
Mohammad Ayman Mursaleen and
Stefano Serra-Capizzano The Eigenvalue Distribution of Special
$2$-by-$2$ Block Matrix-Sequences with
Applications to the Case of Symmetrized
Toeplitz Structures . . . . . . . . . . 1066--1086
Michel Crouzeix and
Anne Greenbaum Spectral Sets: Numerical Range and
Beyond . . . . . . . . . . . . . . . . . 1087--1101
Ron Estrin and
Dominique Orban and
Michael A. Saunders LNLQ: an Iterative Method for Least-Norm
Problems with an Error Minimization
Property . . . . . . . . . . . . . . . . 1102--1124
Mateusz Micha\lek and
Tim Seynnaeve and
Frank Verstraete A Tensor Version of the Quantum Wielandt
Theorem . . . . . . . . . . . . . . . . 1125--1130
Xiaozhe Hu and
Panayot S. Vassilevski Modifying AMG Coarse Spaces with Weak
Approximation Property to Exhibit
Approximation in Energy Norm . . . . . . 1131--1152
Sebastian Krämer A Geometric Description of Feasible
Singular Values in the Tensor Train
Format . . . . . . . . . . . . . . . . . 1153--1178
Antoine Gautier and
Francesco Tudisco and
Matthias Hein The Perron--Frobenius Theorem for
Multihomogeneous Mappings . . . . . . . 1179--1205
Antoine Gautier and
Francesco Tudisco and
Matthias Hein A Unifying Perron--Frobenius Theorem for
Nonnegative Tensors via Multihomogeneous
Maps . . . . . . . . . . . . . . . . . . 1206--1231
Massimiliano Fasi and
Nicholas J. Higham An Arbitrary Precision Scaling and
Squaring Algorithm for the Matrix
Exponential . . . . . . . . . . . . . . 1233--1256
Jesse L. Barlow Block Modified Gram--Schmidt Algorithms
and Their Analysis . . . . . . . . . . . 1257--1290
Vjeran Hari On the Global Convergence of the Complex
HZ Method . . . . . . . . . . . . . . . 1291--1310
Austin R. Benson and
David F. Gleich Computing Tensor $Z$-Eigenvectors with
Dynamical Systems . . . . . . . . . . . 1311--1324
Peter Benner and
Tim Mitchell Extended and Improved Criss-Cross
Algorithms for Computing the Spectral
Value Set Abscissa and Radius . . . . . 1325--1352
Zhenhua Lin Riemannian Geometry of Symmetric
Positive Definite Matrices via Cholesky
Decomposition . . . . . . . . . . . . . 1353--1370
Christopher C. Paige Accuracy of the Lanczos Process for the
Eigenproblem and Solution of Equations 1371--1398
Mykhailo Kuian and
Lothar Reichel and
Sergij Shiyanovskii Optimally Conditioned Vandermonde-Like
Matrices . . . . . . . . . . . . . . . . 1399--1424
Ion Necoara Faster Randomized Block Kaczmarz
Algorithms . . . . . . . . . . . . . . . 1425--1452
Fulvio Gesmundo and
Alessandro Oneto and
Emanuele Ventura Partially Symmetric Variants of Comon's
Problem Via Simultaneous Rank . . . . . 1453--1477
Claude-Pierre Jeannerod and
Theo Mary and
Clément Pernet and
Daniel S. Roche Improving the Complexity of Block
Low-Rank Factorizations with Fast Matrix
Arithmetic . . . . . . . . . . . . . . . 1478--1496
Ruoxi Wang and
Yingzhou Li and
Michael W. Mahoney and
Eric Darve Block Basis Factorization for Scalable
Kernel Evaluation . . . . . . . . . . . 1497--1526
Shenglong Hu and
Defeng Sun and
Kim-Chuan Toh Best Nonnegative Rank-One Approximations
of Tensors . . . . . . . . . . . . . . . 1527--1554
Jane Breen and
Steve Kirkland A Structured Condition Number for
Kemeny's Constant . . . . . . . . . . . 1555--1578
Yu. Nesterov and
V. Yu. Protasov Computing Closest Stable Nonnegative
Matrix . . . . . . . . . . . . . . . . . 1--28
Sophie Hautphenne and
Stefano Massei A Low-Rank Technique for Computing the
Quasi-Stationary Distribution of
Subcritical Galton--Watson Processes . . 29--57
Xiao Liu and
Yuanzhe Xi and
Yousef Saad and
Maarten V. de Hoop Solving the Three-Dimensional
High-frequency Helmholtz Equation Using
Contour Integration and Polynomial
Preconditioning . . . . . . . . . . . . 58--82
Luis García Ramos and
René Kehl and
Reinhard Nabben Projections, Deflation, and Multigrid
for Nonsymmetric Matrices . . . . . . . 83--105
Jaros\law Buczy\'nski and
Elisa Postinghel and
Filip Rupniewski On Strassen's Rank Additivity for Small
Three-way Tensors . . . . . . . . . . . 106--133
Volker Mehrmann and
Paul M. Van Dooren Optimal Robustness of Port-Hamiltonian
Systems . . . . . . . . . . . . . . . . 134--151
Florent Bouchard and
Bijan Afsari and
Jérôme Malick and
Marco Congedo Approximate Joint Diagonalization with
Riemannian Optimization on the General
Linear Group . . . . . . . . . . . . . . 152--170
Estelle Massart and
P.-A. Absil Quotient Geometry with Simple Geodesics
for the Manifold of Fixed-Rank
Positive-Semidefinite Matrices . . . . . 171--198
Dmitry Batenkov and
Laurent Demanet and
Gil Goldman and
Yosef Yomdin Conditioning of Partial Nonuniform
Fourier Matrices with Clustered Nodes 199--220
Xin Xing and
Edmond Chow Interpolative Decomposition via Proxy
Points for Kernel Matrices . . . . . . . 221--243
Yaqi Duan and
Mengdi Wang and
Zaiwen Wen and
Yaxiang Yuan Adaptive Low-Nonnegative-Rank
Approximation for State Aggregation of
Markov Chains . . . . . . . . . . . . . 244--278
Yashar Zeinaly and
Jan H. van Schuppen and
Bart De Schutter Linear Positive Systems May Have a
Reachable Subset from the Origin That is
Either Polyhedral or Nonpolyhedral . . . 279--307
Andrei Agrachev and
Khazhgali Kozhasov and
André Uschmajew Chebyshev Polynomials and Best Rank-one
Approximation Ratio . . . . . . . . . . 308--331
Gilles Baechler and
Frederike Dümbgen and
Golnoosh Elhami and
Miranda Krekovi\'c and
Martin Vetterli Coordinate Difference Matrices . . . . . 332--363
Steven Elsworth and
Stefan Güttel The Block Rational Arnoldi Method . . . 365--388
Martin S. Andersen and
Tianshi Chen Smoothing Splines and Rank Structured
Matrices: Revisiting the Spline Kernel 389--412
Larry Allen and
Robert C. Kirby Structured Inversion of the Bernstein
Mass Matrix . . . . . . . . . . . . . . 413--431
Yao-Lin Jiang and
Kang-Li Xu Riemannian Modified
Polak--Ribi\`ere--Polyak Conjugate
Gradient Order Reduced Model by Tensor
Techniques . . . . . . . . . . . . . . . 432--463
Marie Kubínová and
Kirk M. Soodhalter Admissible and Attainable Convergence
Behavior of Block Arnoldi and GMRES . . 464--486
Peter Richtárik and
Martin Takác Stochastic Reformulations of Linear
Systems: Algorithms and Convergence
Theory . . . . . . . . . . . . . . . . . 487--524
Ximing Chen and
Masaki Ogura and
Victor M. Preciado Bounds on the Spectral Radius of
Digraphs from Subgraph Counts . . . . . 525--553
Pedro G. Massey and
Demetrio Stojanoff and
Sebastian Zarate Majorization Bounds for Ritz Values of
Self-Adjoint Matrices . . . . . . . . . 554--572
Timothy A. Davis and
Iain S. Duff and
Stojce Nakov Design and Implementation of a Parallel
Markowitz Threshold Algorithm . . . . . 573--590
Marina Bertolini and
Gianmario Besana and
Gilberto Bini and
Cristina Turrini The Rank of Trifocal Grassmann Tensors 591--604
Maolin Che and
Yimin Wei and
Hong Yan The Computation of Low Multilinear Rank
Approximations of Tensors via Power
Scheme and Random Projection . . . . . . 605--636
Tobias Damm and
Heike Faßbender Simultaneous Hollowization, Joint
Numerical Range, and Stabilization by
Noise . . . . . . . . . . . . . . . . . 637--656
Fredy Sosa and
Julio Moro and
Christian Mehl First Order Structure-Preserving
Perturbation Theory for Eigenvalues of
Symplectic Matrices . . . . . . . . . . 657--690
Dario A. Bini and
Beatrice Meini and
Jie Meng Solving Quadratic Matrix Equations
Arising in Random Walks in the Quarter
Plane . . . . . . . . . . . . . . . . . 691--714
Léopold Cambier and
Chao Chen and
Erik G. Boman and
Sivasankaran Rajamanickam and
Raymond S. Tuminaro and
Eric Darve An Algebraic Sparsified Nested
Dissection Algorithm Using Low-Rank
Approximations . . . . . . . . . . . . . 715--746
Ignat Domanov and
Lieven De Lathauwer On Uniqueness and Computation of the
Decomposition of a Tensor into
Multilinear Rank-$ (1, L_r, L_r) $ Terms 747--803
Andreas Frommer and
Kathryn Lund and
Daniel B. Szyld Block Krylov Subspace Methods for
Functions of Matrices II: Modified Block
FOM . . . . . . . . . . . . . . . . . . 804--837
Rui Li and
Zeng-Qi Wang Restrictively Preconditioned Conjugate
Gradient Method for a Series of
Constantly Augmented Least Squares
Problems . . . . . . . . . . . . . . . . 838--851
Johannes J. Brust and
Roummel F. Marcia and
Cosmin G. Petra Computationally Efficient Decompositions
of Oblique Projection Matrices . . . . . 852--870
Ben S. Southworth and
Abdullah A. Sivas and
Sander Rhebergen On Fixed-Point, Krylov, and $ 2 \times 2
$ Block Preconditioners for Nonsymmetric
Problems . . . . . . . . . . . . . . . . 871--900
Hongguo Xu A Core-Chasing Symplectic $ Q R $
Algorithm . . . . . . . . . . . . . . . 901--927
Nicat Aliyev and
Peter Benner and
Emre Mengi and
Matthias Voigt A Subspace Framework for $ \mathcal
{H}_\infty $-Norm Minimization . . . . . 928--956
Lei-Hong Zhang and
Wei Hong Yang and
Chungen Shen and
Jiaqi Ying An Eigenvalue-Based Method for the
Unbalanced Procrustes Problem . . . . . 957--983
Roberto Bevilacqua and
Gianna M. Del Corso and
Luca Gemignani Efficient Reduction of Compressed
Unitary Plus Low Rank Matrices to
Hessenberg Form . . . . . . . . . . . . 984--1003
A. S. Lewis and
M. L. Overton Partial Smoothness of the Numerical
Radius at Matrices Whose Fields of
Values are Disks . . . . . . . . . . . . 1004--1032
Fernando De Terán and
Andrii Dmytryshyn and
Froilán M. Dopico Generic Symmetric Matrix Polynomials
with Bounded Rank and Fixed Odd Grade 1033--1058
Xin Ye and
Jianlin Xia and
Lexing Ying Analytical Low-Rank Compression via
Proxy Point Selection . . . . . . . . . 1059--1085
Oscar Mickelin and
Sertac Karaman Multiresolution Low-rank Tensor Formats 1086--1114
Jiawang Nie and
Zi Yang Hermitian Tensor Decompositions . . . . 1115--1144
Alexis Montoison and
Dominique Orban BiLQ: an Iterative Method for
Nonsymmetric Linear Systems with a
Quasi-Minimum Error Property . . . . . . 1145--1166
Aleksandar Cvetkovi\'c and
Vladimir Yu. Protasov Maximal Acyclic Subgraphs and Closest
Stable Matrices . . . . . . . . . . . . 1167--1182
Eric Hallman Sharp $2$-Norm Error Bounds for LSQR and
the Conjugate Gradient Method . . . . . 1183--1207
Anil Damle and
Yuekai Sun Uniform Bounds for Invariant Subspace
Perturbations . . . . . . . . . . . . . 1208--1236
Vincent Coppé and
Daan Huybrechs and
Roel Matthysen and
Marcus Webb The $ A Z $ Algorithm for Least Squares
Systems with a Known Incomplete
Generalized Inverse . . . . . . . . . . 1237--1259
Tianxiang Liu and
Ivan Markovsky and
Ting Kei Pong and
Akiko Takeda A Hybrid Penalty Method for a Class of
Optimization Problems with Multiple Rank
Constraints . . . . . . . . . . . . . . 1260--1283
Wim Michiels and
Luca Fenzi Spectrum-based Stability Analysis and
Stabilization of Time-periodic
Time-delay Systems . . . . . . . . . . . 1284--1311
Jorge Garza-Vargas and
Archit Kulkarni The Lanczos Algorithm Under Few
Iterations: Concentration and Location
of the Output . . . . . . . . . . . . . 1312--1346
Cyrus Mostajeran and
Christian Grussler and
Rodolphe Sepulchre Geometric Matrix Midranges . . . . . . . 1347--1368
Samantha Sherman and
Tamara G. Kolda Estimating Higher-Order Moments Using
Symmetric Tensor Decomposition . . . . . 1369--1387
Carla Ferreira and
Beresford Parlett Eigenpairs of Wilkinson Matrices . . . . 1388--1415
Ziang Chen and
Yingzhou Li and
Jianfeng Lu Tensor Ring Decomposition: Optimization
Landscape and One-loop Convergence of
Alternating Least Squares . . . . . . . 1416--1442
Spyridon Pougkakiotis and
John W. Pearson and
Santolo Leveque and
Jacek Gondzio Fast Solution Methods for Convex
Quadratic Optimization of Fractional
Differential Equations . . . . . . . . . 1443--1476
Silvia Gazzola and
Chang Meng and
James G. Nagy Krylov Methods for Low-Rank
Regularization . . . . . . . . . . . . . 1477--1504
Biswajit Das and
Shreemayee Bora Nearest Matrix Polynomials With a
Specified Elementary Divisor . . . . . . 1505--1527
Frank Uhlig Coalescing Eigenvalues and Crossing
Eigencurves of $1$-Parameter Matrix
Flows . . . . . . . . . . . . . . . . . 1528--1545
Minghua Chen and
Sven-Erik Ekström and
Stefano Serra-Capizzano A Multigrid Method for Nonlocal
Problems: Non-Diagonally Dominant or
Toeplitz-Plus-Tridiagonal Systems . . . 1546--1570
Henri Calandra and
Serge Gratton and
Elisa Riccietti and
Xavier Vasseur On Iterative Solution of the Extended
Normal Equations . . . . . . . . . . . . 1571--1589
Alexander Beigl and
Jarle Sogn and
Walter Zulehner Robust Preconditioners for Multiple
Saddle Point Problems and Applications
to Optimal Control Problems . . . . . . 1590--1615
Miguel D. Bustamante and
Pauline Mellon and
M. Victoria Velasco Solving the Problem of Simultaneous
Diagonalization of Complex Symmetric
Matrices via Congruence . . . . . . . . 1616--1629
Pengzhan Jin and
Yifa Tang and
Aiqing Zhu Unit Triangular Factorization of the
Matrix Symplectic Group . . . . . . . . 1630--1650
Alice Cortinovis and
Daniel Kressner Low-Rank Approximation in the Frobenius
Norm by Column and Row Subset Selection 1651--1673
Andreas Frommer and
Behnam Hashemi Computing Enclosures for the Matrix
Exponential . . . . . . . . . . . . . . 1674--1703
Steffen Börm and
Christina Börst Hybrid Matrix Compression for
High-Frequency Problems . . . . . . . . 1704--1725
Ilse C. F. Ipsen and
Hua Zhou Probabilistic Error Analysis for Inner
Products . . . . . . . . . . . . . . . . 1726--1741
Ke Chen and
Qin Li and
Kit Newton and
Stephen J. Wright Structured Random Sketching for PDE
Inverse Problems . . . . . . . . . . . . 1742--1770
Ding Lu Nonlinear Eigenvector Methods for Convex
Minimization over the Numerical Range 1771--1796
Yuning Yang The Epsilon-Alternating Least Squares
for Orthogonal Low-Rank Tensor
Approximation and Its Global Convergence 1797--1825
Alan Edelman and
Yuyang Wang The GSVD: Where are the Ellipses? Matrix
Trigonometry, and More . . . . . . . . . 1826--1856
Rihuan Ke and
Michael K. Ng and
Ting Wei Efficient Preconditioning for Time
Fractional Diffusion Inverse Source
Problems . . . . . . . . . . . . . . . . 1857--1888
Marija Dodig and
Marko Stosi\'c Rank One Perturbations of Matrix Pencils 1889--1911
Jun Liu and
Shu-Lin Wu A Fast Block $ \alpha $-Circulant
Preconditoner for All-at-Once Systems
From Wave Equations . . . . . . . . . . 1912--1943
Tim Mitchell Computing the Kreiss Constant of a
Matrix . . . . . . . . . . . . . . . . . 1944--1975
Volker Mehrmann and
Paul Van Dooren Structured Backward Errors for
Eigenvalues of Linear Port-Hamiltonian
Descriptor Systems . . . . . . . . . . . 1--16
Simon Barthelmé and
Konstantin Usevich Spectral Properties of Kernel Matrices
in the Flat Limit . . . . . . . . . . . 17--57
Guangjing Song and
Weiyang Ding and
Michael K. Ng Low Rank Pure Quaternion Approximation
for Pure Quaternion Matrices . . . . . . 58--82
Stefan Güttel and
Marcel Schweitzer A Comparison of Limited-memory Krylov
Methods for Stieltjes Functions of
Hermitian Matrices . . . . . . . . . . . 83--107
Petko H. Petkov Componentwise Perturbation Analysis of
the Schur Decomposition of a Matrix . . 108--133
Robert Krone and
Kaie Kubjas Uniqueness of Nonnegative Matrix
Factorizations by Rigidity Theory . . . 134--164
Chao Chen and
Severin Reiz and
Chenhan D. Yu and
Hans-Joachim Bungartz and
George Biros Fast Approximation of the Gauss--Newton
Hessian Matrix for the Multilayer
Perceptron . . . . . . . . . . . . . . . 165--184
Desmond J. Higham and
Nicholas J. Higham and
Srikara Pranesh Random Matrices Generating Large Growth
in $ L U $ Factorization with Pivoting 185--201
Zvonimir Bujanovic and
Daniel Kressner Norm and Trace Estimation with Random
Rank-one Vectors . . . . . . . . . . . . 202--223
Gregory Berkolaiko and
Advait Parulekar Locating Conical Degeneracies in the
Spectra of Parametric Self-adjoint
Matrices . . . . . . . . . . . . . . . . 224--242
Éric Canc\`es and
Gaspard Kemlin and
Antoine Levitt Convergence Analysis of Direct
Minimization and Self-Consistent
Iterations . . . . . . . . . . . . . . . 243--274
Tianyi Shi and
Alex Townsend On the Compressibility of Tensors . . . 275--298
Liqun Qi and
Yannan Chen and
Mayank Bakshi and
Xinzhen Zhang Triple Decomposition and Tensor Recovery
of Third Order Tensors . . . . . . . . . 299--329
Michael S. Floater and
Carla Manni and
Espen Sande and
Hendrik Speleers Best Low-rank Approximations and
Kolmogorov $n$-widths . . . . . . . . . 330--350
Keaton Hamm and
Longxiu Huang Perturbations of CUR Decompositions . . 351--375
Mark A. Iwen and
Deanna Needell and
Elizaveta Rebrova and
Ali Zare Lower Memory Oblivious (Tensor) Subspace
Embeddings with Fewer Random Bits:
Modewise Methods for Least Squares . . . 376--416
Massimiliano Fasi and
Nicholas J. Higham Matrices with Tunable Infinity-Norm
Condition Number and No Need for
Pivoting in $ L U $ Factorization . . . 417--435
Jan Blechta Stability of Linear GMRES Convergence
with Respect to Compact Perturbations 436--447
Ignat Domanov and
Lieven De Lathauwer From Computation to Comparison of Tensor
Decompositions . . . . . . . . . . . . . 449--474
L. Robert Hocking and
Chen Greif Optimal Complex Relaxation Parameters in
Multigrid for Complex-Shifted Linear
Systems . . . . . . . . . . . . . . . . 475--502
M. Christandl and
F. Gesmundo and
M. Micha\lek and
J. Zuiddam Border Rank Nonadditivity for Higher
Order Tensors . . . . . . . . . . . . . 503--527
Antoni Musolas and
Steven T. Smith and
Youssef Marzouk Geodesically Parameterized Covariance
Estimation . . . . . . . . . . . . . . . 528--556
Larry Allen and
Robert C. Kirby Structured Inversion of the
Bernstein--Vandermonde Matrix . . . . . 557--577
Tim Mitchell Fast Interpolation-Based Globality
Certificates for Computing Kreiss
Constants and the Distance to
Uncontrollability . . . . . . . . . . . 578--607
Stefan Steinerberger Randomized Kaczmarz Converges Along
Small Singular Vectors . . . . . . . . . 608--615
ZhiGang Jia and
Michael K. Ng Structure Preserving Quaternion
Generalized Minimal Residual Method . . 616--634
Nela Bosner Parallel Prony's Method with
Multivariate Matrix Pencil Approach and
Its Numerical Aspects . . . . . . . . . 635--658
Qingqing Zheng and
Yuanzhe Xi and
Yousef Saad A Power Schur Complement Low-Rank
Correction Preconditioner for General
Sparse Linear Systems . . . . . . . . . 659--682
Xin Xing and
Hua Huang and
Edmond Chow Efficient Construction of an HSS
Preconditioner for Symmetric Positive
Definite $ \mathcal {H}^2 $ Matrices . . 683--707
Diego Cifuentes A Convex Relaxation to Compute the
Nearest Structured Rank Deficient Matrix 708--729
Valentin Leplat and
Nicolas Gillis and
Jérôme Idier Multiplicative Updates for NMF with $
\beta $-Divergences under Disjoint
Equality Constraints . . . . . . . . . . 730--752
Thijs Steel and
Daan Camps and
Karl Meerbergen and
Raf Vandebril A Multishift, Multipole Rational $ Q Z $
Method with Aggressive Early Deflation 753--774
Emil Ringh and
Elias Jarlebring Nonlinearizing Two-parameter Eigenvalue
Problems . . . . . . . . . . . . . . . . 775--799
Vivak Patel and
Mohammad Jahangoshahi and
Daniel A. Maldonado An Implicit Representation and Iterative
Solution of Randomly Sketched Linear
Systems . . . . . . . . . . . . . . . . 800--831
Chao Zeng and
Michael K. Ng Incremental CP Tensor Decomposition by
Alternating Minimization Method . . . . 832--858
Joong-Ho Won and
Hua Zhou and
Kenneth Lange Orthogonal Trace-Sum Maximization:
Applications, Local Algorithms, and
Global Optimality . . . . . . . . . . . 859--882
Jeroen Vanderstukken and
Lieven De Lathauwer Systems of Polynomial Equations,
Higher-order Tensor Decompositions, and
Multidimensional Harmonic Retrieval: a
Unifying Framework. Part I: The
Canonical Polyadic Decomposition . . . . 883--912
Jeroen Vanderstukken and
Patrick Kürschner and
Ignat Domanov and
Lieven De Lathauwer Systems of Polynomial Equations,
Higher-Order Tensor Decompositions, and
Multidimensional Harmonic Retrieval: a
Unifying Framework. Part II: The Block
Term Decomposition . . . . . . . . . . . 913--953
Robert M. Gower and
Denali Molitor and
Jacob Moorman and
Deanna Needell On Adaptive Sketch-and-Project for
Solving Linear Systems . . . . . . . . . 954--989
Cleve Ashcraft and
Alfredo Buttari and
Theo Mary Block Low-Rank Matrices with Shared
Bases: Potential and Limitations of the
BLR$^2$ Format . . . . . . . . . . . . . 990--1010
Hannes Gernandt and
Frédéric Enrico Haller and
Timo Reis A Linear Relation Approach to
Port-Hamiltonian Differential-Algebraic
Equations . . . . . . . . . . . . . . . 1011--1044
Rachel Minster and
Arvind K. Saibaba and
Jishnudeep Kar and
Aranya Chakrabortty Efficient Algorithms for Eigensystem
Realization Using Randomized SVD . . . . 1045--1072
Gil Shabat and
Era Choshen and
Dvir Ben Or and
Nadav Carmel Fast and Accurate Gaussian Kernel Ridge
Regression Using Matrix Decompositions
for Preconditioning . . . . . . . . . . 1073--1095
Yunhui He A Generalized and Unified Framework of
Local Fourier Analysis Using
Matrix-Stencils . . . . . . . . . . . . 1096--1118
Sohail Bahmani and
Kiryung Lee Low-Rank Matrix Estimation from Rank-One
Projections by Unlifted Convex
Optimization . . . . . . . . . . . . . . 1119--1147
Angelo Casulli and
Leonardo Robol Rank-Structured $ Q R $ for Chebyshev
Rootfinding . . . . . . . . . . . . . . 1148--1171
Peter Benner and
Heike Fassbender and
Philip Saltenberger A Rational Even-IRA Algorithm for the
Solution of $T$-Even Polynomial
Eigenvalue Problems . . . . . . . . . . 1172--1198
Aleksandros Sobczyk and
Efstratios Gallopoulos Estimating Leverage Scores via Rank
Revealing Methods and Randomization . . 1199--1228
Francesca Arrigo and
Desmond J. Higham and
Vanni Noferini A Theory for Backtrack-Downweighted
Walks . . . . . . . . . . . . . . . . . 1229--1247
Xin Ye and
Yuanzhe Xi and
Yousef Saad Proxy-GMRES: Preconditioning via GMRES
in Polynomial Space . . . . . . . . . . 1248--1267
Simon Ruetz and
Karin Schnass Submatrices with NonUniformly Selected
Random Supports and Insights into Sparse
Approximation . . . . . . . . . . . . . 1268--1289
Andreas Frommer and
Claudia Schimmel and
Marcel Schweitzer Analysis of Probing Techniques for
Sparse Approximation and Trace
Estimation of Decaying Matrix Functions 1290--1318
M. Mazza and
J. Pestana The Asymptotic Spectrum of Flipped
Multilevel Toeplitz Matrices and of
Certain Preconditionings . . . . . . . . 1319--1336
Mathias Jacquelin and
Esmond G. Ng and
Barry W. Peyton Fast Implementation of the
Traveling-Salesman-Problem Method for
Reordering Columns within Supernodes . . 1337--1364
Erin Carson and
Kathryn Lund and
Miroslav Rozlozník The Stability of Block Variants of
Classical Gram--Schmidt . . . . . . . . 1365--1380
Keiichi Morikuni Projection Method for Eigenvalue
Problems of Linear Nonsquare Matrix
Pencils . . . . . . . . . . . . . . . . 1381--1400
Nicholas J. Higham and
Xiaobo Liu A Multiprecision Derivative-Free
Schur--Parlett Algorithm for Computing
Matrix Functions . . . . . . . . . . . . 1401--1422
John C. Urschel Uniform Error Estimates for the Lanczos
Method . . . . . . . . . . . . . . . . . 1423--1450
Delin Chu and
Weya Shi and
Srinivas Eswar and
Haesun Park An Alternating Rank-$k$ Nonnegative
Least Squares Framework (ARkNLS) for
Nonnegative Matrix Factorization . . . . 1451--1479
Ronny Ramlau and
Kirk M. Soodhalter and
Victoria Hutterer Subspace Recycling-Based Regularization
Methods . . . . . . . . . . . . . . . . 1480--1505
Pedro Massey and
Demetrio Stojanoff and
Sebastián Zárate Absolute Variation of Ritz Values,
Principal Angles, and Spectral Spread 1506--1527
Silvia Gazzola and
Malena Sabaté Landman Regularization by Inexact Krylov Methods
with Applications to Blind Deblurring 1528--1552
Antonio Fazzi and
Nicola Guglielmi and
Christian Lubich Finding the Nearest Passive or
Nonpassive System via Hamiltonian
Eigenvalue Optimization . . . . . . . . 1553--1580
Francesca Arrigo and
Fabio Durastante Mittag-Leffler Functions and their
Applications in Network Science . . . . 1581--1601
Ines Dorschky and
Timo Reis and
Matthias Voigt Balanced Truncation Model Reduction for
Symmetric Second Order Systems --- a
Passivity-Based Approach . . . . . . . . 1602--1635
Feng Wu and
Kailing Zhang and
Li Zhu and
Jiayao Hu High-Performance Computation of the
Exponential of a Large Sparse Matrix . . 1636--1655
Kevin Burrage and
Pamela Burrage and
Shev Macnamara Localization and Pseudospectra of
Twisted Toeplitz Matrices with
Applications to Ion Channels . . . . . . 1656--1679
Rong Huang Accurate Computation of Generalized
Eigenvalues of Regular SR--BP Pairs . . 1680--1702
Ke Chen and
Ruhui Jin Tensor-Structured Sketching for
Constrained Least Squares . . . . . . . 1703--1731
Nguyen Thanh Son and
P.-A. Absil and
Bin Gao and
Tatjana Stykel Computing Symplectic Eigenpairs of
Symmetric Positive-Definite Matrices via
Trace Minimization and Riemannian
Optimization . . . . . . . . . . . . . . 1732--1757
Björn Liljegren-Sailer and
Nicole Marheineke Input-Tailored System-Theoretic Model
Order Reduction for Quadratic-Bilinear
Systems . . . . . . . . . . . . . . . . 1--39
Xiangmin Jiao and
Qiao Chen Approximate Generalized Inverses with
Iterative Refinement for $ \epsilon
$-Accurate Preconditioning of Singular
Systems . . . . . . . . . . . . . . . . 40--67
Andrew Horning and
Yuji Nakatsukasa Twice Is Enough for Dangerous
Eigenvalues . . . . . . . . . . . . . . 68--93
Abeynaya Gnanasekaran and
Eric Darve Hierarchical Orthogonal Factorization:
Sparse Square Matrices . . . . . . . . . 94--123
Qiaohua Liu and
Zhigang Jia and
Yimin Wei Multidimensional Total Least Squares
Problem with Linear Equality Constraints 124--150
Alice Cortinovis and
Daniel Kressner and
Stefano Massei Divide-and-Conquer Methods for Functions
of Matrices with Banded or Hierarchical
Low-Rank Structure . . . . . . . . . . . 151--177
Ian D. Morris Fast Approximation of the $p$-Radius,
Matrix Pressure, or Generalized Lyapunov
Exponent for Positive and Dominated
Matrices . . . . . . . . . . . . . . . . 178--198
Marianne Akian and
Stéphane Gaubert and
Zheng Qu and
Omar Saadi Multiply Accelerated Value Iteration for
NonSymmetric Affine Fixed Point Problems
and Application to Markov Decision
Processes . . . . . . . . . . . . . . . 199--232
Awad H. Al-Mohy and
Nicholas J. Higham and
Xiaobo Liu Arbitrary Precision Algorithms for
Computing the Matrix Cosine and its
Fréchet Derivative . . . . . . . . . . . 233--256
Ragnhild Laursen and
Asger Hobolth A Sampling Algorithm to Compute the Set
of Feasible Solutions for NonNegative
Matrix Factorization with an Arbitrary
Rank . . . . . . . . . . . . . . . . . . 257--273
Eric Evert and
Michiel Vandecappelle and
Lieven De Lathauwer A Recursive Eigenspace Computation for
the Canonical Polyadic Decomposition . . 274--300
Zhaojun Bai and
Ren-Cang Li and
Ding Lu Sharp Estimation of Convergence Rate for
Self-Consistent Field Iteration to Solve
Eigenvector-Dependent Nonlinear
Eigenvalue Problems . . . . . . . . . . 301--327
Eric Evert and
Lieven De Lathauwer Guarantees for Existence of a Best
Canonical Polyadic Approximation of a
Noisy Low-Rank Tensor . . . . . . . . . 328--369
Yongyan Guo and
Gang Wu A New Lower Bound on the Size of the
Smallest Vertex Separator of a Graph . . 370--376
Sarah Dendievel and
Guy Latouche and
Yuanyuan Liu and
Yingchun Tang Singularly Perturbed Markov Modulated
Fluid Queues . . . . . . . . . . . . . . 377--404
Matthias Bolten and
Marco Donatelli and
Paola Ferrari and
Isabella Furci A Symbol-Based Analysis for Multigrid
Methods for Block-Circulant and
Block-Toeplitz Systems . . . . . . . . . 405--438
Christopher J. Lourenco and
Erick Moreno-Centeno Exactly Solving Sparse Rational Linear
Systems via Roundoff-Error-Free Cholesky
Factorizations . . . . . . . . . . . . . 439--463
Harry Yserentant A Measure Concentration Effect for
Matrices of High, Higher, and Even
Higher Dimension . . . . . . . . . . . . 464--478
Paz Fink Shustin and
Haim Avron Semi-Infinite Linear Regression and Its
Applications . . . . . . . . . . . . . . 479--511
Xuefeng Xu and
Chen-Song Zhang A New Analytical Framework for the
Convergence of Inexact Two-Grid Methods 512--533
Wei-Wei Xu and
Michael K. Ng and
Zheng-Jian Bai Geometric Inexact Newton Method for
Generalized Singular Values of Grassmann
Matrix Pair . . . . . . . . . . . . . . 535--560
Scott P. MacLachlan and
Niall Madden and
Thái Anh Nhan A Boundary-Layer Preconditioner for
Singularly Perturbed Convection
Diffusion . . . . . . . . . . . . . . . 561--583
Zhongxiao Jia Theoretical and Computable Optimal
Subspace Expansions for Matrix
Eigenvalue Problems . . . . . . . . . . 584--604
Jamie Haddock and
Deanna Needell and
Elizaveta Rebrova and
William Swartworth Quantile-Based Iterative Methods for
Corrupted Systems of Linear Equations 605--637
Stefano Massei and
Leonardo Robol Mixed Precision Recursive Block
Diagonalization for Bivariate Functions
of Matrices . . . . . . . . . . . . . . 638--660
Eric Hallman A Block Bidiagonalization Method for
Fixed-Accuracy Low-Rank Matrix
Approximation . . . . . . . . . . . . . 661--680
Jesse L. Barlow and
Stanley C. Eisenstat and
Nevena Jakovcevi\'c Stor and
Ivan Slapnicar Deflation for the Symmetric Arrowhead
and Diagonal-Plus-Rank-One Eigenvalue
Problems . . . . . . . . . . . . . . . . 681--709
Luc Giraud and
Yan-Fei Jing and
Yanfei Xiang A Block Minimum Residual Norm Subspace
Solver with Partial Convergence
Management for Sequences of Linear
Systems . . . . . . . . . . . . . . . . 710--739
Anshul Prajapati and
Punit Sharma Estimation of Structured Distances to
Singularity for Matrix Pencils with
Symmetry Structures: a Linear
Algebra--Based Approach . . . . . . . . 740--763
Rob Claes and
Elias Jarlebring and
Karl Meerbergen and
Parikshit Upadhyaya Linearizable Eigenvector Nonlinearities 764--786
Tyler Chen and
Anne Greenbaum and
Cameron Musco and
Christopher Musco Error Bounds for Lanczos-Based Matrix
Function Approximation . . . . . . . . . 787--811
Xiaojing Jia and
Xin Liang and
Chungen Shen and
Lei-Hong Zhang Solving the Cubic Regularization Model
by a Nested Restarting Lanczos Method 812--839
Shuyu Dong and
Bin Gao and
Yu Guan and
François Glineur New Riemannian Preconditioned Algorithms
for Tensor Completion via Polyadic
Decomposition . . . . . . . . . . . . . 840--866
Xiaoyu Song and
Baodong Zheng and
Riguang Huang Maximal Rank of $ m \times n \times 2 $
Tensors over Arbitrary Fields . . . . . 867--881
Thanh Hieu Le and
Thi Ngan Nguyen Simultaneous Diagonalization via
Congruence of Hermitian Matrices: Some
Equivalent Conditions and a Numerical
Solution . . . . . . . . . . . . . . . . 882--911
Nithin Govindarajan and
Ethan N. Epperly and
Lieven De Lathauwer $ (L_r, L_r, 1) $-Decompositions, Sparse
Component Analysis, and the Blind
Separation of Sums of Exponentials . . . 912--938
Tim Fuchs and
David Gross and
Felix Krahmer and
Richard Kueng and
Dustin Mixon Sketching with Kerdock's Crayons: Fast
Sparsifying Transforms for Arbitrary
Linear Maps . . . . . . . . . . . . . . 939--952
Ralf Zimmermann and
Knut Hüper Computing the Riemannian Logarithm on
the Stiefel Manifold: Metrics, Methods,
and Performance . . . . . . . . . . . . 953--980
Itziar Baragaña and
Alicia Roca On the Change of the Weyr
Characteristics of Matrix Pencils After
Rank-One Perturbations . . . . . . . . . 981--1002
Difeng Cai and
James Nagy and
Yuanzhe Xi Fast Deterministic Approximation of
Symmetric Indefinite Kernel Matrices
with High Dimensional Datasets . . . . . 1003--1028
Tomohiko Mizutani Refinement of Hottopixx Method for
Nonnegative Matrix Factorization Under
Noisy Separability . . . . . . . . . . . 1029--1057
Peter Benner and
Yuji Nakatsukasa and
Carolin Penke Stable and Efficient Computation of
Generalized Polar Decompositions . . . . 1058--1083
Daan Camps and
Efekan Kökcü and
Lindsay Bassman Oftelie and
Wibe A. de Jong and
Alexander F. Kemper and
Roel Van Beeumen An Algebraic Quantum Circuit Compression
Algorithm for Hamiltonian Simulation . . 1084--1108
Jacqueline Wentz and
Jeffrey C. Cameron and
David M. Bortz Analytical Singular Value Decomposition
for a Class of Stoichiometry Matrices 1109--1147
Luca Dieci and
Alessandra Papini and
Alessandro Pugliese Takagi Factorization of Matrices
Depending on Parameters and Locating
Degeneracies of Singular Values . . . . 1148--1161
David Persson and
Alice Cortinovis and
Daniel Kressner Improved Variants of the Hutch++
Algorithm for Trace Estimation . . . . . 1162--1185
C. Mehl and
V. Mehrmann and
M. Wojtylak Matrix Pencils with Coefficients that
have Positive Semidefinite Hermitian
Parts . . . . . . . . . . . . . . . . . 1186--1212
Froilán M. Dopico and
María C. Quintana and
Paul Van Dooren Diagonal Scalings for the Eigenstructure
of Arbitrary Pencils . . . . . . . . . . 1213--1237
Gabriel Oksa and
Yusaku Yamamoto and
Marián Vajtersic Convergence to Singular Triplets in the
Two-Sided Block-Jacobi SVD Algorithm
with Dynamic Ordering . . . . . . . . . 1238--1262
Ethan N. Epperly and
Lin Lin and
Yuji Nakatsukasa A Theory of Quantum Subspace
Diagonalization . . . . . . . . . . . . 1263--1290
Yuan Jian Subspaces Analysis for Random Projection
UTV Framework . . . . . . . . . . . . . 1291--1307
Kensuke Aihara and
Akira Imakura and
Keiichi Morikuni Cross-Interactive Residual Smoothing for
Global and Block Lanczos-Type Solvers
for Linear Systems with Multiple
Right-Hand Sides . . . . . . . . . . . . 1308--1330
Shu-Lin Wu and
Tao Zhou and
Zhi Zhou A Uniform Spectral Analysis for a
Preconditioned All-at-Once System from
First-Order and Second-Order
Evolutionary Problems . . . . . . . . . 1331--1353
Froilán M. Dopico and
María C. Quintana and
Paul Van Dooren Strongly Minimal Self-Conjugate
Linearizations for Polynomial and
Rational Matrices . . . . . . . . . . . 1354--1381
Elias Jarlebring and
Siobhán Correnty Infinite GMRES for Parameterized Linear
Systems . . . . . . . . . . . . . . . . 1382--1405
Serge Gratton and
Ehouarn Simon and
David Titley-Peloquin and
Philippe L. Toint A Note on Inexact Inner Products in
GMRES . . . . . . . . . . . . . . . . . 1406--1422
Edward Poon and
Ilya M. Spitkovsky and
Hugo J. Woerdeman Factorization of Singular Matrix
Polynomials and Matrices with Circular
Higher Rank Numerical Ranges . . . . . . 1423--1439
Nidham Gazagnadou and
Mark Ibrahim and
Robert M. Gower RidgeSketch: a Fast Sketching Based
Solver for Large Scale Ridge Regression 1440--1468
Giorgio Cipolloni and
László Erdös and
Dominik Schröder On the Condition Number of the Shifted
Real Ginibre Ensemble . . . . . . . . . 1469--1487
Brett W. Larsen and
Tamara G. Kolda Practical Leverage-Based Sampling for
Low-Rank Tensor Decomposition . . . . . 1488--1517
Radu Balan and
Chris B. Dock Lipschitz Analysis of Generalized Phase
Retrievable Matrix Frames . . . . . . . 1518--1571
Maseim Kenmoe and
Ronald Kriemann and
Matteo Smerlak and
Anton S. Zadorin A Fast Iterative Algorithm for
Near-Diagonal Eigenvalue Problems . . . 1573--1598
Misha E. Kilmer and
Arvind K. Saibaba Structured Matrix Approximations via
Tensor Decompositions . . . . . . . . . 1599--1626
James Brannick and
Shuhao Cao A Bootstrap Multigrid Eigensolver . . . 1627--1657
Frantisek Stampach Asymptotic Spectral Properties of the
Hilbert $L$-Matrix . . . . . . . . . . . 1658--1679
Samah Karim and
Edgar Solomonik Efficient Preconditioners for Interior
Point Methods via a New Schur
Complement-Based Strategy . . . . . . . 1680--1711
Guiyun Xiao and
Zheng-Jian Bai and
Wai-Ki Ching A Columnwise Update Algorithm for Sparse
Stochastic Matrix Factorization . . . . 1712--1735
Siegfried M. Rump Verified Error Bounds for All
Eigenvalues and Eigenvectors of a Matrix 1736--1754
Hans De Sterck and
Yunhui He Linear Asymptotic Convergence of
Anderson Acceleration: Fixed-Point
Analysis . . . . . . . . . . . . . . . . 1755--1783
Tommi Muller and
Elina Robeva and
Konstantin Usevich Robust Eigenvectors of Symmetric Tensors 1784--1805
Stefan Bamberger and
Felix Krahmer and
Rachel Ward Johnson--Lindenstrauss Embeddings with
Kronecker Structure . . . . . . . . . . 1806--1850
Yann Thanwerdas and
Xavier Pennec Theoretically and Computationally
Convenient Geometries on Full-Rank
Correlation Matrices . . . . . . . . . . 1851--1872
Yunhui He and
Jun Liu Smoothing Analysis of Two Robust
Multigrid Methods for Elliptic Optimal
Control Problems . . . . . . . . . . . . 1--26
Nicolas Gillis and
Róbert Rajkó Partial Identifiability for Nonnegative
Matrix Factorization . . . . . . . . . . 27--52
Iveta Hnetynková and
Martin Plesinger and
Jana Záková Krylov Subspace Approach to Core
Problems within Multilinear
Approximation Problems: a Unifying
Framework . . . . . . . . . . . . . . . 53--79
Moon Duchin and
James M. Murphy and
Thomas Weighill Measuring Segregation via Analysis on
Graphs . . . . . . . . . . . . . . . . . 80--105
Matthias Beaup\`ere and
David Frenkiel and
Laura Grigori Higher-Order $ Q R $ with Tournament
Pivoting for Tensor Compression . . . . 106--127
Klemens Fritzsche and
Klaus Röbenack Unimodular Completions and Orthogonal
Complements of Matrices over Univariate
Ore Extensions . . . . . . . . . . . . . 128--155
Massimiliano Fasi and
Nicholas J. Higham and
Xiaobo Liu Computing the Square Root of a Low-Rank
Perturbation of the Scaled Identity
Matrix . . . . . . . . . . . . . . . . . 156--174
Milan Hladík Properties of the Solution Set of
Absolute Value Equations and the Related
Matrix Classes . . . . . . . . . . . . . 175--195
Yaokun Wu and
Yinfeng Zhu Primitivity and Hurwitz Primitivity of
Nonnegative Matrix Tuples: a Unified
Approach . . . . . . . . . . . . . . . . 196--211
Changpeng Shao A Deterministic Kaczmarz Algorithm for
Solving Linear Systems . . . . . . . . . 212--239
Eric Hallman and
Ilse C. F. Ipsen and
Arvind K. Saibaba Monte Carlo Methods for Estimating the
Diagonal of a Real Symmetric Matrix . . 240--269
Tomohiro Sugiyama and
Kazuhiro Sato Kron Reduction and Effective Resistance
of Directed Graphs . . . . . . . . . . . 270--292
Alexis Montoison and
Dominique Orban GPMR: an Iterative Method for
Unsymmetric Partitioned Linear Systems 293--311
Nicholas F. Marshall and
Oscar Mickelin An Optimal Scheduled Learning Rate for a
Randomized Kaczmarz Algorithm . . . . . 312--330
Pieter Appeltans and
Wim Michiels A Structure Preserving Shift-Invert
Infinite Arnoldi Algorithm for a Class
of Delay Eigenvalue Problems with
Hamiltonian Symmetry . . . . . . . . . . 331--358
Valeria Simoncini and
Yue Hao Analysis of the Truncated Conjugate
Gradient Method for Linear Matrix
Equations . . . . . . . . . . . . . . . 359--381
Zhongxiao Jia and
Haibo Li The Joint Bidiagonalization Method for
Large GSVD Computations in Finite
Precision . . . . . . . . . . . . . . . 382--407
James Demmel Nearly Optimal Block-Jacobi
Preconditioning . . . . . . . . . . . . 408--413
Alan Edelman and
Sungwoo Jeong Fifty Three Matrix Factorizations: a
Systematic Approach . . . . . . . . . . 415--480
Meiyue Shao Householder Orthogonalization with a
Nonstandard Inner Product . . . . . . . 481--502
Quoc-Tung Le and
Elisa Riccietti and
Remi Gribonval Spurious Valleys, NP-Hardness, and
Tractability of Sparse Matrix
Factorization with Fixed Support . . . . 503--529
Zheng-Hai Huang and
Yu-Fan Li and
Xinhe Miao Finding the Least Element of a
Nonnegative Solution Set of a Class of
Polynomial Inequalities . . . . . . . . 530--558
James Demmel and
Laura Grigori and
Alexander Rusciano An Improved Analysis and Unified
Perspective on Deterministic and
Randomized Low-Rank Matrix Approximation 559--591
Jianze Li and
Konstantin Usevich and
Pierre Comon Convergence of Gradient-Based Block
Coordinate Descent Algorithms for
Nonorthogonal Joint Approximate
Diagonalization of Matrices . . . . . . 592--621
Angela Fontan and
Claudio Altafini Pseudoinverses of Signed Laplacian
Matrices . . . . . . . . . . . . . . . . 622--647
Diego Altafini and
Dario A. Bini and
Valerio Cutini and
Beatrice Meini and
Federico Poloni An Edge Centrality Measure Based on the
Kemeny Constant . . . . . . . . . . . . 648--669
Tyler Chen and
Anne Greenbaum and
Cameron Musco and
Christopher Musco Low-Memory Krylov Subspace Methods for
Optimal Rational Matrix Function
Approximation . . . . . . . . . . . . . 670--692
A. Frommer and
K. Kahl and
M. Schweitzer and
M. Tsolakis Krylov Subspace Restarting for Matrix
Laplace Transforms . . . . . . . . . . . 693--717
Zachary Frangella and
Joel A. Tropp and
Madeleine Udell Randomized Nyström Preconditioning . . . 718--752
Tim Mitchell and
Paul Van Dooren Root-Max Problems, Hybrid
Expansion-Contraction, and Quadratically
Convergent Optimization of Passive
Systems . . . . . . . . . . . . . . . . 753--780
Yifeng Fan and
Yuehaw Khoo and
Zhizhen Zhao A Spectral Method for Joint Community
Detection and Orthogonal Group
Synchronization . . . . . . . . . . . . 781--821
Fangzheng Xie Euclidean Representation of Low-Rank
Matrices and Its Geometric Properties 822--866
Eric Evert and
Lieven De Lathauwer On Best Low Rank Approximation of
Positive Definite Tensors . . . . . . . 867--893
David Persson and
Daniel Kressner Randomized Low-Rank Approximation of
Monotone Matrix Functions . . . . . . . 894--918
Shengyu Cao and
Simai He and
Zhening Li and
Zhen Wang Extreme Ratio Between Spectral and
Frobenius Norms of Nonnegative Tensors 919--944
John Peca-Medlin and
Thomas Trogdon Growth Factors of Random Butterfly
Matrices and the Stability of Avoiding
Pivoting . . . . . . . . . . . . . . . . 945--970
Cory D. Hauck and
Stefan Schnake A Predictor-Corrector Strategy for
Adaptivity in Dynamical Low-Rank
Approximations . . . . . . . . . . . . . 971--1005
Charles Colley and
Huda Nassar and
David F. Gleich Dominant $Z$-Eigenpairs of Tensor
Kronecker Products Decouple . . . . . . 1006--1031
Christopher Brissette and
Andy Huang and
George Slota Spectrum Consistent Coarsening
Approximates Edge Weights . . . . . . . 1032--1046
Idris Kempf and
Paul J. Goulart and
Stephen R. Duncan A Higher-Order Generalized Singular
Value Decomposition for Rank-Deficient
Matrices . . . . . . . . . . . . . . . . 1047--1072
Stefan Güttel and
Marcel Schweitzer Randomized Sketching for Krylov
Approximations of Large-Scale Matrix
Functions . . . . . . . . . . . . . . . 1073--1095
João Gouveia and
Bruno F. Lourenço Self-Dual Polyhedral Cones and Their
Slack Matrices . . . . . . . . . . . . . 1096--1121
Jinpeng Liu and
Yuanyuan Liu and
Yiqiang Q. Zhao Matrix-Analytic Methods for Solving
Poisson's Equation with Applications to
Markov Chains of GI/G/1-Type . . . . . . 1122--1145
Michael P. Connolly and
Nicholas J. Higham Probabilistic Rounding Error Analysis of
Householder QR Factorization . . . . . . 1146--1163
Vanni Noferini and
Paul Van Dooren Revisiting the Matrix Polynomial
Greatest Common Divisor . . . . . . . . 1164--1188
Kang Zhao and
Zhong Y. Liu Eigenvalue Embedding of Damped
Vibroacoustic System with No-Spillover 1189--1217
Tyler Chen and
Eric Hallman Krylov-Aware Stochastic Trace Estimation 1218--1244
Peter Benner and
Yuji Nakatsukasa and
Carolin Penke A Structure-Preserving
Divide-and-Conquer Method for
Pseudosymmetric Matrices . . . . . . . . 1245--1270
Jon Donnelly and
Peter Stechlinski Analyzing the Influence of Agents in
Trust Networks: Applying Nonsmooth
Eigensensitivity Theory to a Graph
Centrality Problem . . . . . . . . . . . 1271--1298
Vanni Noferini and
Lauri Nyman and
Javier Pérez and
María C. Quintana Perturbation Theory of Transfer Function
Matrices . . . . . . . . . . . . . . . . 1299--1320
Marcel Schweitzer Sensitivity of Matrix Function Based
Network Communicability Measures:
Computational Methods and A Priori
Bounds . . . . . . . . . . . . . . . . . 1321--1348
Vivak Patel and
Mohammad Jahangoshahi and
D. Adrian Maldonado Randomized Block Adaptive Linear System
Solvers . . . . . . . . . . . . . . . . 1349--1369
Yuji Nakatsukasa and
Taejun Park Randomized Low-Rank Approximation for
Symmetric Indefinite Matrices . . . . . 1370--1392
Junjun Pan and
Michael K. Ng Coseparable Nonnegative Matrix
Factorization . . . . . . . . . . . . . 1393--1420
Guillaume Olikier and
P.-A. Absil An Apocalypse-Free First-Order Low-Rank
Optimization Algorithm with at Most One
Rank Reduction Attempt per Iteration . . 1421--1435
Stefan Steinerberger Approximate Solutions of Linear Systems
at a Universal Rate . . . . . . . . . . 1436--1446
Yann Thanwerdas and
Xavier Pennec Bures--Wasserstein Minimizing Geodesics
between Covariance Matrices of Different
Ranks . . . . . . . . . . . . . . . . . 1447--1476
Sean Hon and
Jiamei Dong and
Stefano Serra-Capizzano A Preconditioned MINRES Method for
Optimal Control of Wave Equations and
its Asymptotic Spectral Distribution
Theory . . . . . . . . . . . . . . . . . 1477--1509
H. Gernandt and
F. Martínez Pería and
F. Philipp and
C. Trunk On Characteristic Invariants of Matrix
Pencils and Linear Relations . . . . . . 1510--1539
Chen Greif and
Yunhui He Block Preconditioners for the
Marker-and-Cell Discretization of the
Stokes--Darcy Equations . . . . . . . . 1540--1565
Anna Ma and
Dominik Stöger and
Yizhe Zhu Robust Recovery of Low-Rank Matrices and
Low-Tubal-Rank Tensors from Noisy
Sketches . . . . . . . . . . . . . . . . 1566--1588
Michiel E. Hochstenbach and
Christian Mehl and
Bor Plestenjak Solving Singular Generalized Eigenvalue
Problems. Part II: Projection and
Augmentation . . . . . . . . . . . . . . 1589--1618
Rob Claes and
Karl Meerbergen and
Simon Telen Contour Integration for Eigenvector
Nonlinearities . . . . . . . . . . . . . 1619--1644
Manuel Radons and
Josué Tonelli-Cueto Generalized Perron Roots and Solvability
of the Absolute Value Equation . . . . . 1645--1666
Anwa Zhou and
Kun Liu and
Jinyan Fan Semidefinite Relaxation Methods for
Tensor Absolute Value Equations . . . . 1667--1692
Mareike Dressler and
André Uschmajew and
Venkat Chandrasekaran Kronecker Product Approximation of
Operators in Spectral Norm via
Alternating SDP . . . . . . . . . . . . 1693--1708
Zihao Li and
Lek-Heng Lim Generalized Matrix Nearness Problems . . 1709--1730
Philip A. Knight and
Luce le Gorrec and
Sandrine Mouysset and
Daniel Ruiz Introducing the Class of SemiDoubly
Stochastic Matrices: a Novel Scaling
Approach for Rectangular Matrices . . . 1731--1748
Zhen-Chen Guo and
Xin Liang Stochastic Algebraic Riccati Equations
Are Almost as Easy as Deterministic Ones
Theoretically . . . . . . . . . . . . . 1749--1770
Shu-Lin Wu and
Zhiyong Wang and
Tao Zhou PinT Preconditioner for Forward-Backward
Evolutionary Equations . . . . . . . . . 1771--1798
Philipp Dettling and
Roser Homs and
Carlos Améndola and
Mathias Drton and
Niels Richard Hansen Identifiability in Continuous Lyapunov
Models . . . . . . . . . . . . . . . . . 1799--1821
Luke Cooper and
Jeremy Sumner Uniformization Stable Markov Models and
Their Jordan Algebraic Structure . . . . 1822--1851
Ming Zhou and
Merico Argentati and
Andrew V. Knyazev and
Klaus Neymeyr Sharp Majorization-Type Cluster Robust
Bounds for Block Filters and
Eigensolvers . . . . . . . . . . . . . . 1852--1878
Marija Dodig and
Marko Sto i Bounded Rank Perturbations of
Quasi-Regular Pencils Over Arbitrary
Fields . . . . . . . . . . . . . . . . . 1879--1907
Ethan N. Epperly and
Joel A. Tropp and
Robert J. Webber XTrace: Making the Most of Every Sample
in Stochastic Trace Estimation . . . . . 1--23
Zhongxiao Jia and
Kailiang Zhang An Augmented Matrix-Based CJ-FEAST
SVDsolver for Computing a Partial
Singular Value Decomposition with the
Singular Values in a Given Interval . . 24--58
Tsung-Ming Huang and
Yueh-Cheng Kuo and
Wen-Wei Lin and
Shih-Feng Shieh Structure-Preserving Doubling Algorithms
That Avoid Breakdowns for Algebraic
Riccati-Type Matrix Equations . . . . . 59--83
Zhaojun Bai and
Ding Lu Variational Characterization of Monotone
Nonlinear Eigenvector Problems and
Geometry of Self-Consistent Field
Iteration . . . . . . . . . . . . . . . 84--111
Lars Eldén Multiway Spectral Graph Partitioning:
Cut Functions, Cheeger Inequalities, and
a Simple Algorithm . . . . . . . . . . . 112--133
Jan Modersitzki The Spectral Decomposition of the
Continuous and Discrete Linear
Elasticity Operators with Sliding
Boundary Conditions . . . . . . . . . . 134--147
Patrick Amestoy and
Olivier Boiteau and
Alfredo Buttari and
Matthieu Gerest and
Fabienne Jézéquel and
Jean-Yves L. Excellent and
Theo Mary Communication Avoiding Block Low-Rank
Parallel Multifrontal Triangular Solve
with Many Right-Hand Sides . . . . . . . 148--166
Wentao Ding and
Jianze Li and
Shuzhong Zhang Projectively and Weakly Simultaneously
Diagonalizable Matrices and their
Applications . . . . . . . . . . . . . . 167--202
Andrei Dumitrasc and
Carola Kruse and
Ulrich Rüde Deflation for the Off-Diagonal Block in
Symmetric Saddle Point Systems . . . . . 203--231
Haibo Li The Joint Bidiagonalization of a Matrix
Pair with Inaccurate Inner Iterations 232--259
Fernando De Terán and
Andrii Dmytryshyn and
Froilán M. Dopico Generic Eigenstructures of Hermitian
Pencils . . . . . . . . . . . . . . . . 260--283
Manuel Bogoya and
Sergei M. Grudsky and
Stefano Serra-Capizzano Fast Non-Hermitian Toeplitz Eigenvalue
Computations, Joining Matrixless
Algorithms and FDE Approximation
Matrices . . . . . . . . . . . . . . . . 284--305
Tao Li and
Qing-Wen Wang Structure Preserving Quaternion
Biconjugate Gradient Method . . . . . . 306--326
James Jackaman and
Scott MacLachlan Constraint-Satisfying Krylov Solvers for
Structure-Preserving Discretizations . . 327--352
François Charton and
Kristin Lauter and
Cathy Li and
Mark Tygert An Efficient Algorithm for Integer
Lattice Reduction . . . . . . . . . . . 353--367
Nithin Govindarajan and
Raphaël Widdershoven and
Shivkumar Chandrasekaran and
Lieven De Lathauwer A Fast Algorithm for Computing Macaulay
Null Spaces of Bivariate Polynomial
Systems . . . . . . . . . . . . . . . . 368--396
Francesca Arrigo and
Desmond J. Higham and
Vanni Noferini and
Ryan Wood Weighted Enumeration of Nonbacktracking
Walks on Weighted Graphs . . . . . . . . 397--418
Yaroslav Shitov More on Tensors with Different Rank and
Symmetric Rank . . . . . . . . . . . . . 419--428
Alan Edelman and
Ekin Akyürek and
Yuyang Wang Backpropagation through Back
Substitution with a Backslash . . . . . 429--449
Hussam Al Daas and
Grey Ballard and
Laura Grigori and
Suraj Kumar and
Kathryn Rouse Communication Lower Bounds and Optimal
Algorithms for Multiple
Tensor-Times-Matrix Computation . . . . 450--477
Agurtzane Amparan and
Itziar Baragaña and
Silvia Marcaida and
Alicia Roca Row or Column Completion of Polynomial
Matrices of Given Degree . . . . . . . . 478--503
Emanuel H. Rubensson A Unifying Framework for Higher Order
Derivatives of Matrix Functions . . . . 504--528
Patrick Amestoy and
Alfredo Buttari and
Nicholas J. Higham and
Jean-Yves L. Excellent and
Theo Mary and
Bastien Vieublé Five-Precision GMRES-Based Iterative
Refinement . . . . . . . . . . . . . . . 529--552
Joost Berkhout and
Bernd Heidergott and
Paul Van Dooren Perturbation and Inverse Problems of
Stochastic Matrices . . . . . . . . . . 553--584
Jairo Bochi and
Piotr Laskawiec Spectrum Maximizing Products Are Not
Generically Unique . . . . . . . . . . . 585--600
Susana Furtado and
Charles Johnson Efficient Vectors for Block Perturbed
Consistent Matrices . . . . . . . . . . 601--618
Alice Cortinovis and
Daniel Kressner and
Yuji Nakatsukasa Speeding Up Krylov Subspace Methods for
Computing $ f(A) b $ via Randomization 619--633
Tong Wei and
Weiyang Ding and
Yimin Wei Singular Value Decomposition of Dual
Matrices and its Application to
Traveling Wave Identification in the
Brain . . . . . . . . . . . . . . . . . 634--660
Haoze He and
Daniel Kressner Randomized Joint Diagonalization of
Symmetric Matrices . . . . . . . . . . . 661--684
Zachary M. Boyd and
Nicolas Fraiman and
Jeremy L. Marzuola and
Peter J. Mucha and
Braxton Osting An Escape Time Formulation for Subgraph
Detection and Partitioning of Directed
Graphs . . . . . . . . . . . . . . . . . 685--711
Huan He and
Ziyuan Tang and
Shifan Zhao and
Yousef Saad and
Yuanzhe Xi nlTGCR: a Class of Nonlinear
Acceleration Procedures Based on
Conjugate Residuals . . . . . . . . . . 712--743
Kai Bergermann and
Martin Stoll Adaptive Rational Krylov Methods for
Exponential Runge--Kutta Integrators . . 744--770
Matthias Christandl and
Fulvio Gesmundo and
Vladimir Lysikov and
Vincent Steffan Partial Degeneration of Tensors . . . . 771--800
Daan Camps and
Lin Lin and
Roel Van Beeumen and
Chao Yang Explicit Quantum Circuits for Block
Encodings of Certain Sparse Matrices . . 801--827
Christopher C. Paige Analyzing Vector Orthogonalization
Algorithms . . . . . . . . . . . . . . . 829--846
Vincent Griem and
Sabine Le Borne A Block Householder-Based Algorithm for
the $ Q R $ Decomposition of
Hierarchical Matrices . . . . . . . . . 847--874
Fabio Durastante and
Beatrice Meini Stochastic $p$ th Root Approximation of
a Stochastic Matrix: a Riemannian
Optimization Approach . . . . . . . . . 875--904
Maike Meier and
Yuji Nakatsukasa and
Alex Townsend and
Marcus Webb Are Sketch-and-Precondition Least
Squares Solvers Numerically Stable? . . 905--929
Yann Thanwerdas Permutation-Invariant Log-Euclidean
Geometries on Full-Rank Correlation
Matrices . . . . . . . . . . . . . . . . 930--953
Awad H. Al-Mohy Conditioning of Matrix Functions at
Quasi-Triangular Matrices . . . . . . . 954--966
Alan Edelman and
John Urschel Some New Results on the Maximum Growth
Factor in Gaussian Elimination . . . . . 967--991
El Houcine Bergou and
Soumia Boucherouite and
Aritra Dutta and
Xin Li and
Anna Ma A Note on the Randomized Kaczmarz
Algorithm for Solving Doubly Noisy
Linear Systems . . . . . . . . . . . . . 992--1006
Ivo Dravins and
Stefano Serra-Capizzano and
Maya Neytcheva Spectral Analysis of Preconditioned
Matrices Arising from Stage-Parallel
Implicit Runge--Kutta Methods of
Arbitrarily High Order . . . . . . . . . 1007--1034
Peter Benner and
Pawan Goyal and
Paul Van Dooren Parameterized Interpolation of Passive
Systems . . . . . . . . . . . . . . . . 1035--1053
Mohammad Hamed and
Reshad Hosseini Riemannian Preconditioned Coordinate
Descent for Low Multilinear Rank
Approximation . . . . . . . . . . . . . 1054--1075
Qinmeng Zou Probabilistic Rounding Error Analysis of
Modified Gram--Schmidt . . . . . . . . . 1076--1088
Cyrus Mostajeran and
Nathaël Da Costa and
Graham Van Goffrier and
Rodolphe Sepulchre Differential Geometry with Extreme
Eigenvalues in the Positive Semidefinite
Cone . . . . . . . . . . . . . . . . . . ??
Jinzhi Huang and
Zhongxiao Jia A Skew-Symmetric Lanczos
Bidiagonalization Method for Computing
Several Extremal Eigenpairs of a Large
Skew-Symmetric Matrix . . . . . . . . . ??
Andreas A. Bock and
Martin S. Andersen Preconditioner Design via Bregman
Divergences . . . . . . . . . . . . . . ??
Yuji Nakatsukasa and
Joel A. Tropp Fast and Accurate Randomized Algorithms
for Linear Systems and Eigenvalue
Problems . . . . . . . . . . . . . . . . ??
Milan Hladík Erratum: Properties of the Solution Set
of Absolute Value Equations and the
Related Matrix Classes . . . . . . . . . ??
Ziang Chen and
Jianfeng Lu and
Anru Zhang One-Dimensional Tensor Network Recovery ??
Ben S. Southworth and
Thomas A. Manteuffel On Compatible Transfer Operators in
Nonsymmetric Algebraic Multigrid . . . . ??
Yun Zeng and
Deren Han and
Yansheng Su and
Jiaxin Xie On Adaptive Stochastic Heavy Ball
Momentum for Solving Linear Systems . . ??
Satin K. Gungah and
Fawwaz F. Alsubaie and
Imad M. Jaimoukha On the Two-Parameter Matrix Pencil
Problem . . . . . . . . . . . . . . . . ??
Ignat Domanov and
Nico Vervliet and
Eric Evert and
Lieven De Lathauwer Decomposition of a Tensor into
Multilinear Rank-$ (M_r, N_r, \cdot) $
Terms . . . . . . . . . . . . . . . . . ??
Volker Mehrmann and
Hongguo Xu Eigenstructure Perturbations for a Class
of Hamiltonian Matrices and Solutions of
Related Riccati Inequalities . . . . . . ??
Erin Carson and
Ieva Dauzickaite Single-Pass Nyström Approximation in
Mixed Precision . . . . . . . . . . . . ??
Michael Stewart Spectral Transformation for the Dense
Symmetric Semidefinite Generalized
Eigenvalue Problem . . . . . . . . . . . ??
Shmuel Friedland and
Chi-Kwong Li On Semidefinite Programming
Characterizations of the Numerical
Radius and Its Dual Norm . . . . . . . . ??
Junjun Pan and
Michael K. Ng Block-Diagonalization of Quaternion
Circulant Matrices with Applications . . ??
Tianyi Lu and
Yangfeng Su and
Zhaojun Bai Variational Characterization and
Rayleigh Quotient Iteration of $2$D
Eigenvalue Problem with Applications . . ??
Jesse L. Barlow Reorthogonalized Block Classical
Gram--Schmidt Using Two Cholesky-Based
TSQR Algorithms . . . . . . . . . . . . ??
Christos Boutsikas and
Petros Drineas and
Ilse C. F. Ipsen Small Singular Values Can Increase in
Lower Precision . . . . . . . . . . . . ??
Alexander Cloninger and
Gal Mishne and
Andreas Oslandsbotn and
Sawyer J. Robertson and
Zhengchao Wan and
Yusu Wang Random Walks, Conductance, and
Resistance for the Connection Graph
Laplacian . . . . . . . . . . . . . . . ??
Teodor Bucht and
Jacob S. Christiansen A Geometric Approach to Approximating
the Limit Set of Eigenvalues for Banded
Toeplitz Matrices . . . . . . . . . . . ??
John Peca-Medlin Growth Factors of Orthogonal Matrices
and Local Behavior of Gaussian
Elimination with Partial and Complete
Pivoting . . . . . . . . . . . . . . . . ??