% This is the AmSTeX SIAM style file, (amstex)siam.sty.
%  RCS information: $Revision: 1.3 $, $Date: 90/01/31 11:15:14 $.
%  Authors: Bradley J. Lucier and Douglas N. Arnold.
%  Copyright 1988, 1990 by Bradley Lucier.  All rights reserved.
%
% You have permission to copy this file, to use it as input to other TeX
% files, and to modify it as necessary to allow it to run at your site.
% In the interest of maintaining a consistent revision history, if you
% make changes, additions, or deletions to this file, you must indicate
% how the changes affected the original file, so that the original file
% can be reconstructed if necessary.  Possible changes include: changing
% all fonts to the Almost computer Modern fonts, changing the position of
% the printing on the page with hoffset and voffset, and changing the
% definition of \eightsmc to a font that is available at your site.
%
% To suggest changes for future versions of siam.sty or make other
% comments, contact
%
%   Prof. B. Lucier
%   Department of Mathematics
%   Purdue University
%   West Lafayette, IN   47907
%     lucier@cs.purdue.edu
%
% This is an unofficial siam style file for AmSTeX, version 1.0 or
% later.  It has been used to produce papers for SIAM journals that have
% been totally acceptable to the SIAM production editors.  There is a set
% of instructions for using this style file to produce documents that are
% very similar to papers in SIAM journals.  To obtain a copy, send the
% message
%
% send amstex from typesetting.
%
% to research!netlib, netlib@research.att.com, or netlib@ornl.gov, or
% contact
%
%   Prof. D. Arnold
%   Department of Mathematics
%   The Pennsylvania State University
%   University Park, PA 16802
%      dna@math.psu.edu
%
% This style file is unsupported.
\catcode`\@=11
\ifx\siamloaded@AmS\relax\catcode`\@=\active
 \endinput\else\let\siamloaded@AmS\relax\fi
\W@{This is an AmS-TeX compatible SIAM style file.}
\W@{Copyright 1988 by Bradley Lucier.}
\W@{This style file can be used only under the terms contained in the file.}
\hsize 31 pc \hcorrection{0.6666666 in}
\vsize 49.5 pc \vcorrection{0.3333333 in}
\topskip=12pt
\normallineskiplimit\p@
\captionwidth@\hsize
\advance\captionwidth@-1.5in
\font@\ninerm=cmr9
\font@\eightrm=cmr8
\font@\sixrm=cmr6
\font@\ninei=cmmi9    \skewchar\ninei='177
\font@\eighti=cmmi8   \skewchar\eighti='177
\font@\sixi=cmmi6     \skewchar\sixi='177
\font@\ninesy=cmsy9   \skewchar\ninesy='60
\font@\eightsy=cmsy8  \skewchar\eightsy='60
\font@\sixsy=cmsy6    \skewchar\sixsy='60
\font@\ninebf=cmbx9
\font@\eightbf=cmbx8
\font@\sixbf=cmbx6
\font@\nineit=cmti9
\font@\eightit=cmti8
\font@\ninesl=cmsl9
\font@\eightsl=cmsl8
\font@\ninemsx=msxm9
\font@\eightmsx=msxm8
\font@\sixmsx=msxm6
\font@\ninemsy=msym9
\font@\eightmsy=msym8
\font@\sixmsy=msym6
\font@\tensmc=cmcsc10
\font@\eightsmc=cmcsc10 scaled 800
\parindent 2 em
\def\tenpoint{\def\pointsize@{10}%
 \normalbaselineskip12\p@
 \abovedisplayskip12\p@ plus3\p@ minus9\p@
 \belowdisplayskip12\p@ plus3\p@ minus9\p@
 \abovedisplayshortskip\z@ plus3\p@
 \belowdisplayshortskip7\p@ plus3\p@ minus4\p@
 \textfont@\rm\tenrm
 \textfont@\it\tenit
 \textfont@\sl\tensl
 \textfont@\bf\tenbf
 \textfont@\smc\tensmc
 \ifsyntax@\def\big##1{{\hbox{$\left##1\right.$}}}\else
 \let\big\tenbig@
 \textfont\z@\tenrm  \scriptfont\z@\sevenrm  \scriptscriptfont\z@\fiverm
 \textfont\@ne\teni  \scriptfont\@ne\seveni  \scriptscriptfont\@ne\fivei
 \textfont\tw@\tensy \scriptfont\tw@\sevensy \scriptscriptfont\tw@\fivesy
 \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
 \textfont\itfam\tenit
 \textfont\slfam\tensl
 \textfont\bffam\tenbf \scriptfont\bffam\sevenbf
  \scriptscriptfont\bffam\fivebf
 \textfont\msxfam=\tenmsx
 \scriptfont\msxfam=\sevenmsx
 \scriptscriptfont\msxfam=\fivemsx
 \textfont\msyfam=\tenmsy
 \scriptfont\msyfam=\sevenmsy
 \scriptscriptfont\msyfam=\fivemsy
 \fi
 \setbox\strutbox\hbox{\vrule height8.5\p@ depth3.5\p@ width\z@}%
 \setbox\strutbox@\hbox{\vrule height8\p@ depth3\p@ width\z@}%
 \normalbaselines\tenrm\ex@=.2326ex}
\def\eightpoint{\def\pointsize@{8}%
 \normalbaselineskip10\p@
 \abovedisplayskip10\p@ plus2.4\p@ minus7.2\p@
 \belowdisplayskip10\p@ plus2.4\p@ minus7.2\p@
 \abovedisplayshortskip\z@ plus2.4\p@
 \belowdisplayshortskip5.6\p@ plus2.4\p@ minus3.2\p@
 \textfont@\rm\eightrm
 \textfont@\it\eightit
 \textfont@\sl\eightsl
 \textfont@\bf\eightbf
 \textfont@\smc\eightsmc
 \ifsyntax@\def\big##1{{\hbox{$\left##1\right.$}}}\else
 \let\big\eightbig@
 \textfont\z@\eightrm \scriptfont\z@\sixrm  \scriptscriptfont\z@\fiverm
 \textfont\@ne\eighti \scriptfont\@ne\sixi  \scriptscriptfont\@ne\fivei
 \textfont\tw@\eightsy \scriptfont\tw@\sixsy \scriptscriptfont\tw@\fivesy
 \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
 \textfont\itfam\eightit
 \textfont\slfam\eightsl
 \textfont\bffam\eightbf \scriptfont\bffam\sixbf
   \scriptscriptfont\bffam\fivebf
 \textfont\msxfam=\eightmsx
 \scriptfont\msxfam=\sixmsx
 \scriptscriptfont\msxfam=\fivemsx
 \textfont\msyfam=\eightmsy
 \scriptfont\msyfam=\sixmsy
 \scriptscriptfont\msyfam=\fivemsy
 \fi
 \setbox\strutbox\hbox{\vrule height7\p@ depth3\p@ width\z@}%
 \setbox\strutbox@\hbox{\vrule height6.5\p@ depth2.5\p@ width\z@}%
 \normalbaselines\eightrm\ex@=.2326ex}
\def\tenbig@#1{{\hbox{$\left#1\vbox to8.5\p@{}\right.\n@space$}}}
\def\eightbig@#1{{\hbox{$\textfont\z@\ninerm\textfont\tw@\ninesy
 \left#1\vbox to6.5\p@{}\right.\n@space$}}}
\def\footmarkform@#1{$^{#1}$}
\let\thefootnotemark\footmarkform@
\def\makefootnote@#1#2{\insert\footins
 {\interlinepenalty\interfootnotelinepenalty
 \eightpoint\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox
 \floatingpenalty\@MM\leftskip\z@\rightskip\z@\spaceskip\z@\xspaceskip\z@
 \indent{#1}\footstrut\ignorespaces#2\unskip\lower\dp\strutbox
 \vbox to\dp\strutbox{}}}
\footmarkcount@\z@
\def\footnotemark{\let\@sf\empty\relaxnext@\ifhmode\edef
 \@sf{\spacefactor\the\spacefactor}\/\fi
 \def\next@{\ifx[\next\let\next\nextii@\else
  \ifx"\next\let\next\nextiii@\else
  \let\next\nextiv@\fi\fi\next}%
 \def\nextii@[##1]{\footmarkform@{##1}\@sf}%
 \def\nextiii@"##1"{{##1}\@sf}%
 \def\nextiv@{\global\advance\footmarkcount@\@ne
  \footmarkform@{\number\footmarkcount@}\@sf}%
 \futurelet\next\next@}
\def\footnotetext{\relaxnext@
 \def\next@{\ifx[\next\let\next\nextii@\else
  \ifx"\next\let\next\nextiii@\else
  \let\next\nextiv@\fi\fi\next}%
 \def\nextii@[##1]##2{\makefootnote@{\footmarkform@{##1}}{##2}}%
 \def\nextiii@"##1"##2{\makefootnote@{##1}{##2}}%
 \def\nextiv@##1{\makefootnote@{\footmarkform@{\number\footmarkcount@}}{##1}}%
 \futurelet\next\next@}
\def\footnote{\let\@sf\empty\relaxnext@\ifhmode\edef
 \@sf{\spacefactor\the\spacefactor}\/\fi
 \def\next@{\ifx[\next\let\next\nextii@\else
  \ifx"\next\let\next\nextiii@\else
  \let\next\nextiv@\fi\fi\next}%
 \def\nextii@[##1]##2{\footnotemark[##1]\footnotetext[##1]{##2}}%
 \def\nextiii@"##1"##2{\footnotemark"##1"\footnotetext"##1"{##2}}%
 \def\nextiv@##1{\footnotemark\footnotetext{##1}}%
 \futurelet\next\next@}
\def\adjustfootnotemark#1{\advance\footmarkcount@#1\relax}
\def\topmatter
  {\normallineskip0pt\normallineskiplimit0pt\parskip0pt\normalbaselines}
\newbox\titlebox@
\setbox\titlebox@\vbox{}
\Invalid@\overlong
\def\overlong@{\def\next@{\ifx\next\overlong\def\filhss@
 {plus\@m\p@ minus\@m\p@}\def\next@\overlong{\nextii@}\else
 \def\filhss@{plus\@m\p@\relax}\let\next@\nextii@\fi\next@}}
\def\title{\relaxnext@
 \def\nextii@##1\endtitle{{\def\\{\cr\strut}
 \global\setbox\titlebox@\vbox{\tabskip\z@\filhss@
 \halign to\hsize{\tenpoint\bf\hfil\ignorespaces####\unskip
  \hfil\cr\strut##1\cr}}}}%
 \overlong@
 \futurelet\next\next@}
\newif\ifauthor@
\newbox\authorbox@
\def\author{\relaxnext@
 \def\nextii@##1\endauthor{{\def\\{\cr\strut}
 \global\setbox\authorbox@\vbox{\tabskip\z@\filhss@
 \halign to\hsize{\eightpoint\smc\hfil\ignorespaces####\unskip\hfil\cr
  \strut##1\cr}}}}\overlong@\global\author@true
 \futurelet\next\next@}
\def\affil{\Err@{Do not use \string\affil\space in the siam style}}
\def\endaffil{\Err@{Do not use \string\endaffil\space in the siam style}}
\def\address{\Err@{Do not use \string\address\space in the siam style}}
\def\date{\Err@{Do not use \string\date\space in the siam style}}
\def\thanks{\Err@{Do not use \string\thanks\space in the siam style}}
\Invalid@\nofrills
\Invalid@\usualspace
\newif\ifnofrills@
\def\usualspace@#1{\ifnofrills@\def\usualspace{#1}\fi}
\def\nofrills@#1#2{\def\next@{\ifx\next\nofrills\nofrills@true\let#2\relax
 \def\next@\nofrills{\nextii@}\else\nofrills@false
 \def#2{#1}\let\next@\nextii@\fi\next@}}
\def\proclaim{\innerproclaim@}
\def\endproclaim{\innerendproclaim@}
\newif\ifabstract@
\def\theabstract@{}
\def\abstract{\relaxnext@\nofrills@{{\bf Abstract.\enspace}}\abstract@
 \long\def\nextii@##1{\long\gdef\theabstract@{\usualspace@
  {{\eightpoint\enspace}}\eightpoint\abstract@\ignorespaces##1\par}}%
 \global\abstract@true
 \futurelet\next\next@}
\newif\ifkeywords@
\def\thekeywords@{}
\def\keywords{\relaxnext@\nofrills@{{\bf Key words.\enspace}}\keywords@
 \long\def\nextii@##1{\long\gdef\thekeywords@{\usualspace@
    {{\eightpoint\enspace}}\eightpoint\keywords@\ignorespaces##1\par}}%
 \global\keywords@true
 \futurelet\next\next@}
\newif\ifsubjclass@
\def\thesubjclass@{}
\def\subjclass{\relaxnext@\nofrills@{{\bf
  AMS(MOS) subject classifications.\enspace}}\subjclass@
 \long\def\nextii@##1{\long\gdef\thesubjclass@{\usualspace@
    {{\eightpoint\enspace}}\eightpoint\subjclass@\ignorespaces##1\par}}%
 \global\subjclass@true
 \futurelet\next\next@}
\def\pretitle{}
\def\preauthor{}
\def\preabstract{}
\def\prekeywords{}
\def\presubjclass{}
\def\prepaper{}
\def\endtopmatter{\hrule height\z@\vskip-\topskip
 \pretitle
 \vskip16\p@ %
 \unvbox\titlebox@
 \preauthor
 \ifauthor@\vskip7.5\p@%
     {\unvbox\authorbox@}\fi
 \preabstract
 \ifabstract@\vskip14\p@%
     {\eightpoint\indent\strut\theabstract@}\fi
 \prekeywords
 \ifkeywords@\vskip 8 pt%
  {\eightpoint\indent\strut\thekeywords@}\fi
 \presubjclass
 \ifsubjclass@\vskip 8 pt%
  {\eightpoint\indent\strut\thesubjclass@}\fi
 \prepaper
 \outer\def\proclaim{\innerproclaim@}%
 \outer\def\endproclaim{\innerendproclaim@}%
 \vskip8\p@%
 \parskip=0 pt plus 1 pt
 \normallineskiplimit=1pt\normallineskip=1pt
     \tenpoint}
\outer\def\enddocument{\vfill\supereject\end}
\newbox\headingbox@
\outer\def\heading{\relaxnext@
 \def\nextii@{\bigbreak\bgroup\let\\=\cr
 \global\setbox\headingbox@\vbox\bgroup\tabskip\z@\filhss@
 \halign to\hsize\bgroup\tenpoint\smc\hfil\ignorespaces####\unskip\hfil\cr}%
 \overlong@
 \futurelet\next\next@}
\def\endheading{\cr\egroup\egroup\egroup\unvbox\headingbox@
 \nobreak\medskip}
\def\subheading{\relaxnext@\nofrills@{.\enspace}\subheading@
 \def\nextii@##1{\medbreak\indent{\usualspace@{{\bf\enspace}}%
  \tenpoint\bf\ignorespaces##1\unskip\subheading@}\ignorespaces}%
 \futurelet\next\next@}
\newif\ifproclaim@
\def\innerproclaim@{\relaxnext@\nofrills@{.\enspace}\proclaim@
 \def\nextii@##1{\par\def\next{8}%
  {\usualspace@{{\smc\enspace}}\smc\ignorespaces##1\unskip\proclaim@}\it
  \ifproclaim@\Err@{Previous \expandafter
 \eat@\string\\proclaim has no matching \expandafter
 \eat@\string\\endproclaim}\else\proclaim@true\fi\ignorespaces}%
 \futurelet\next\next@}
\def\innerendproclaim@{\proclaim@false\par\rm
 }
\def\demo{\relaxnext@\nofrills@{.\enspace}\demo@
 \def\nextii@##1{\par{\usualspace@{{\it\enspace}}%
  \it\ignorespaces##1\unskip\demo@}\rm
  \ifproclaim@\Err@{Previous \expandafter
  \eat@\string\\proclaim had no matching \expandafter
  \eat@\string\\endproclaim}\fi\ignorespaces}%
 \futurelet\next\next@}
\def\enddemo{\par}
\def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5\p@\fi\fi
 \hbox{\hskip5\p@\lower 1.5 pt\hbox{\vrule width .2 pt
 \vbox{\hrule width 4 pt height .2 pt \vskip 7.1 pt
 \hrule width 4 pt height .2 pt }\unskip\vrule width .2 pt}\hskip\p@}}
\def\cite#1{\relaxnext@
 \def\nextiii@##1,##2\end@{[{\rm##1},##2]}%
 \in@,{#1}\ifin@\def\next{\nextiii@#1\end@}\else
 \def\next{[{\rm#1}]}\fi\next}
\newcount\rostercount@
\newdimen\rosterindent
\newdimen\rosterindent@
\newdimen\labelwidth@
\rosterindent=20 pt
\rosterindent@=20 pt
\newif\iffirstitem@
\newtoks\everypartoks@
\let\plainitem@\item
\def\par@{\everypartoks@=\expandafter{\the\everypar}\everypar{}}
\def\roster{\global\advance\rosterindent@\rosterindent
  \labelwidth@=\rosterindent@
 \advance\labelwidth@-7.222222 pt\relax
 \edef\leftskip@{\leftskip\the\leftskip}\relaxnext@
 \rostercount@\z@\def\item{\futurelet\next\rosteritem@}%
 \def\next@{\ifx\next\runinitem\let\next\nextii@\else
  \let\next\nextiii@\fi\next}%
 \def\nextii@\runinitem{\unskip
  \def\next@{\ifx\next[\let\next\nextii@\else
   \ifx\next"\let\next\nextiii@\else\let\next\nextiv@\fi\fi\next}%
  \def\nextii@[####1]{\rostercount@####1\relax
   \enspace{\rm(\number\rostercount@)}~\ignorespaces}%
  \def\nextiii@"####1"{\enspace{\rm####1}~\ignorespaces}%
  \def\nextiv@{\enspace{\rm(1)}\rostercount@\@ne~}%
  \par@\firstitem@false
  \futurelet\next\next@}%
 \def\nextiii@{\par\par@\penalty\@m
  \firstitem@true}%
 \futurelet\next\next@}
\def\rosteritem@{\iffirstitem@\firstitem@false\else\par\fi
 \leftskip\rosterindent@\noindent
 \def\next@[##1]{\rostercount@##1\relax
  \llap{\hbox to\labelwidth@{\hss\rm(\number\rostercount@)}\hskip
  7.222222 pt}\ignorespaces}%
 \def\nextii@"##1"{%
  \llap{\hbox to\labelwidth@{\hss\rm##1}\hskip7.222222 pt}\ignorespaces}%
 \def\nextiii@{\advance\rostercount@\@ne
  \llap{\hbox to\labelwidth@{\hss\rm(\number\rostercount@)}\hskip
  7.222222 pt}}%
 \ifx\next[\let\next\next@\else\ifx\next"\let\next\nextii@\else
 \let\next\nextiii@\fi\fi\next}
\def\therosteritem#1{{\rm(\ignorespaces#1\unskip)}}
\newif\ifnextRunin@
\def\endroster{\global\advance\rosterindent@-\rosterindent\relax
 \relaxnext@\par\leftskip@
 \penalty-50 \vskip\parskip
 \def\next@{\ifx\next\Runinitem\let\next@\relax
  \else\nextRunin@false\let\item\plainitem@\ifx\next\par
  \def\next@\par{\everypar=\expandafter{\the\everypartoks@}}%
  \else\def\next@{\noindent\everypar=\expandafter{\the\everypartoks@}}%
  \fi\fi\next@}%
 \futurelet\next\next@}
\newcount\rosterhangafter@
\def\Runinitem#1\roster\runinitem{\relaxnext@\rostercount@\z@
 \def\item{\futurelet\next\rosteritem@}%
 \def\runinitem@{#1}%
 \def\next@{\ifx\next[\let\next\nextii@\else\ifx\next"\let\next\nextiii@
  \else\let\next\nextiv@\fi\fi\next}%
 \def\nextii@[##1]{\rostercount@##1\relax\def\item@{{\rm(\number
  \rostercount@)}}\nextv@}%
 \def\nextiii@"##1"{\def\item@{{\rm##1}}\nextv@}%
 \def\nextiv@{\advance\rostercount@\@ne\def\item@{{\rm(\number
  \rostercount@)}}\nextv@}%
 \def\nextv@{\setbox\z@\vbox
  {\ifnextRunin@\noindent\fi
  \runinitem@\unskip\enspace\item@~\par
  \global\rosterhangafter@\prevgraf}%
  \firstitem@false\ifnextRunin@\else\par\fi
  \hangafter\rosterhangafter@\hangindent\rosterindent@
  \ifnextRunin@\noindent\fi\runinitem@\unskip\enspace
  \item@~\ifnextRunin@\else\par@\fi\nextRunin@true\ignorespaces}%
 \futurelet\next\next@}
\outer\def\Refs{\relaxnext@\def\refskip@{\hskip\@ne sp\hskip\m@ne sp}%
 \def\next@{\ifx\next\nofrills\def\next@\nofrills{\nextii@}\else
  \def\next@{\nextii@{REFERENCES}}\fi\next@}%
 \def\nextii@##1{\vskip 24 pt\goodbreak\hbox to\hsize{\hfil\eightpoint
  \rm\ignorespaces##1\unskip\hfil}\nobreak
  \vskip 8 pt\eightpoint\sfcode`.=\@m}%
 \futurelet\next\next@}
\newbox\nobox@        \newbox\keybox@        \newbox\bybox@
\newbox\bysamebox@    \newbox\paperbox@      \newbox\paperinfobox@
\newbox\jourbox@      \newbox\volbox@        \newbox\issuebox@
\newbox\yrbox@                               \newbox\pagesbox@
\newbox\bookbox@
\newbox\bookinfobox@  \newbox\publbox@       \newbox\publaddrbox@
\newbox\finalinfobox@
\newif\ifno@          \newif\ifkey@          \newif\ifby@ \newif\ifmanyby@
\newif\ifbysame@      \newif\ifpaper@        \newif\ifpaperinfo@
\newif\ifjour@        \newif\ifvol@          \newif\ifissue@
\newif\ifyr@ \newif\iftoappear@              \newif\ifpages@ \newif\ifpage@
\newif\ifbook@ \newif\ifinbook@
\newif\ifbookinfo@    \newif\ifpubl@         \newif\ifpubladdr@
\newif\iffinalinfo@   \newif\ifafterbook@
\newif\iffirstref@    \newif\iflastref@      \newif\ifprevjour@
\newif\ifprevbook@    \newif\ifprevinbook@   \newif\ifnojourinfo@
\newdimen\maxbysamerule@
\maxbysamerule@3 em
\def\ref@{\global\no@false\global\key@false\global\by@false
 \global\bysame@false\global\paper@false\global\paperinfo@false
 \global\jour@false\global\vol@false\global\issue@false
 \global\yr@false\global\toappear@false\global\pages@false\global\page@false
 \global\book@false\global\inbook@false
 \global\bookinfo@false\global\publ@false\global\publaddr@false
 \global\finalinfo@false
 \bgroup\ignorespaces}
\Invalid@\moreref
\outer\def\ref{\begingroup
 \noindent\hangindent 42 pt\hangafter\@ne\firstref@true
 \lastref@false\def\moreref{\egroup\endref@\global\firstref@false\ref@}\ref@}
\def\refdef@#1#2{\def#1{\egroup
 \csname\expandafter\eat@\string#1@true\endcsname
 \expandafter\setbox
 \csname\expandafter\eat@\string#1box@\endcsname\hbox\bgroup#2}}
\refdef@\no\relax \refdef@\key\relax
\def\manyby{\egroup\global\manyby@true\by@true\setbox\bybox@\hbox\bgroup\smc}
\def\by{\egroup\by@true\bysame@false\global\manyby@false
 \setbox\bybox@\hbox\bgroup\smc}
\def\bysame{\egroup\bysame@true\bgroup}
\refdef@\paper\it
\refdef@\paperinfo\relax
\def\jour{\egroup\jour@true\prevjour@true\setbox
 \jourbox@\hbox\bgroup}
\refdef@\vol\rm
\refdef@\issue\relax \refdef@\yr\relax
\def\toappear{\egroup\toappear@true\bgroup}
\refdef@\pages\relax
\def\page{\egroup\page@true\setbox\pagesbox@\hbox\bgroup}
\refdef@\book\it
\def\inbook{\egroup\inbook@true\previnbook@true\setbox
 \bookbox@\hbox\bgroup\rm}
\refdef@\bookinfo\relax
\refdef@\publ\relax
\refdef@\publaddr\relax
\refdef@\finalinfo\relax
\def\setpunct@{\def\prepunct@{\ifnum\lastpenalty<0
 \edef\penalty@{\penalty\the\lastpenalty}\unpenalty,
  \penalty@\relax\space\else
 \ifdim\lastskip=\@ne sp\unskip\unskip
 \edef\penalty@{\penalty\the\lastpenalty}\unpenalty,
  \penalty@\relax\space
 \else,\space\fi\fi\afterbook@false}}
\def\ppunbox@#1{\prepunct@\unhbox#1\unskip}
\def\endref@{\let\prepunct@\relax
 \iffirstref@
  \ifno@\hbox to 27 pt {\hss[\unhbox\nobox@\unskip]\kern 8.5 pt}\else
  \ifkey@\hbox to 27 pt{\hss\unhbox\keybox@\unskip\kern 8.5pt}\else
   \hbox to 8.5pt {}\fi\fi
  \ifmanyby@
   \ifby@\hbox{\unhcopy\bybox@\unskip}\setpunct@
  \global\setbox\bysamebox@\hbox{\unhcopy\bybox@\unskip}\else
  \ifbysame@\ifdim\wd\bysamebox@>\maxbysamerule@
    \hbox to\maxbysamerule@{\leaders\hrule height 2.2pt depth -2pt\hfill}\else
    \hbox to \wd\bysamebox@{\leaders\hrule height 2.2pt depth -2pt\hfill}\fi
     \setpunct@\fi
   \fi
  \else
  \ifby@\unhcopy\bybox@\unskip\setpunct@\fi\fi
 \fi
 \ifpaper@\ppunbox@\paperbox@\setpunct@\fi
 \ifpaperinfo@\ppunbox@\paperinfobox@\setpunct@\fi
 \ifjour@\ppunbox@\jourbox@\setpunct@
   \ifvol@\ppunbox@\volbox@\unskip\setpunct@\fi
   \ifissue@\ \unhbox\issuebox@\unskip\setpunct@\fi
   \ifyr@\ (\unhbox\yrbox@\unskip)\setpunct@\fi
   \iftoappear@\ (to appear)\setpunct@\fi
   \ifpages@\prepunct@ pp.\ \unhbox\pagesbox@\unskip\setpunct@\fi
   \ifpage@\prepunct@ p.\ \unhbox\pagesbox@\unskip\setpunct@\fi
 \else
  \ifprevjour@\unskip\nojourinfo@false
   \ifvol@\else\ifissue@\else\ifyr@\else\nojourinfo@true\fi\fi\fi
   \ifnojourinfo@\else,\fi
   \ifvol@\ppunbox@\volbox@\unskip\setpunct@\fi
   \ifissue@\ \unhbox\issuebox@\unskip\setpunct@\fi
   \ifyr@\ (\unhbox\yrbox@\unskip)\setpunct@\fi
   \iftoappear@\ (to appear)\setpunct@\fi
   \ifpages@\prepunct@ pp.\ \unhbox\pagesbox@\unskip\setpunct@\fi
   \ifpage@\prepunct@ p.\ \unhbox\pagesbox@\unskip\setpunct@\fi
  \fi
 \fi
 \ifbook@\prepunct@\unhbox\bookbox@\unskip\afterbook@true\setpunct@\fi
 \ifinbook@\prepunct@\unskip\ in \unhbox\bookbox@\unskip\afterbook@true
  \setpunct@\global\book@true\fi
 \ifbookinfo@\ppunbox@\bookinfobox@\setpunct@\fi
 \ifpubl@\ppunbox@\publbox@\setpunct@\fi
 \ifpubladdr@\ppunbox@\publaddrbox@\setpunct@\fi
 \ifbook@
  \ifyr@\prepunct@\unhbox\yrbox@\unskip\setpunct@\fi
  \iftoappear@\ifafterbook@\fi\prepunct@ to appear\afterbook@false
   \setpunct@\fi
  \ifpages@\prepunct@ pp.\ \unhbox\pagesbox@\unskip\setpunct@\fi
  \ifpage@\prepunct@ p.\ \unhbox\pagesbox@\unskip\setpunct@\fi
 \else
  \ifprevinbook@\unskip
   \ifyr@\prepunct@\unhbox\yrbox@\unskip\setpunct@\fi
   \iftoappear@\prepunct@ to appear\setpunct@\fi
   \ifpages@\prepunct@ pp.\ \unhbox\pagesbox@\unskip\setpunct@\fi
   \ifpage@\prepunct@ p.\ \unhbox\pagesbox@\unskip\setpunct@\fi
  \fi
 \fi
\iffinalinfo@.\afterbook@false
\spacefactor3000\relax\space\unhbox\finalinfobox@\else
 \iflastref@.\afterbook@false\else;
  \afterbook@false\space\fi
\fi}
\def\endref{\egroup\global\lastref@true\endref@\global\prevjour@false\global
 \previnbook@false\par\endgroup}
\newif\iffirstpage@
\firstpage@true
\newif\ifaccepted@
\def\accepted{\accepted@true}
\accepted@false
\output={\output@}
\def\output@{%
\iffirstpage@\global\firstpage@false\shipout
 \vbox{\ifaccepted@\global\pageno=\firstpageno\vbox to 2 pc
 {\baselineskip=8pt\vss
  \hbox to \hsize{\sixrm\journalname\hfill{\textfont\tw@\sixsy
  \copyright}\ \issueyear\ Society for Industrial and Applied Mathematics}
  \hbox to \hsize{\sixrm Vol.~\issuevolume, No.~\issuenumber,
    pp.~\firstpageno--\lastpageno, \issuemonth\ \issueyear\hfill
    \placenumber}\vskip-\prevdepth\vskip 8 pt}\else\vbox
    {\vrule height 2 pc width 0 pt}\fi\nointerlineskip
  \vbox to\vsize
  {\boxmaxdepth\maxdepth\pagecontents}\nointerlineskip\vbox to 16 pt{\vss
  \hbox to \hsize{\eightpoint\hfill\number\pageno\hfill}}}%
 \else
 \shipout\vbox{\vbox to 2 pc{\baselineskip=12pt
  \vss\ifodd\pageno
   \hbox to \hsize{\tenpoint\relaxnext@\phantom{\number\pageno}\hfil
   {\smc\oddhead}\hfil\number\pageno}
  \else
   \hbox to \hsize{\tenpoint\number\pageno\hfil{\smc\evenhead}\hfil\relaxnext@
   \phantom{\number\pageno}}\fi\vskip-\prevdepth\vskip 12 pt}\nointerlineskip%
  \vbox to\vsize
  {\boxmaxdepth\maxdepth\pagecontents}}%
 \fi
 \global\advance\pageno\@ne
 \ifnum\outputpenalty>-\@MM\else\dosupereject\fi}
\def\firstpageno{1}
\def\lastpageno{0}
\def\journalname{}
\def\issuevolume{}
\def\issuenumber{}
\def\issuemonth{}
\def\placenumber{}
\def\issueyear{}
\def\oddhead{}
\def\evenhead{}
\def\footnoterule{\hrule width 36 pt height .2 pt \vskip 2.8\p@}
\skip\footins=12 pt plus 18 pt minus 6 pt
\tenpoint
\catcode`\@=\active
\def\styname{siam}\def\styversion{1.1}