numeric::gtdata
-- weights and
abscissae of Gauss-Tschebyscheff quadraturenumeric::gtdata
(n)
returns the weights and
the abscissae of the Gauss-Tschebyscheff quadrature rule with
n nodes.
numeric::gtdata(n)
n |
- | the number of nodes: a positive integer |
A list [b,c]
is returned. The lists
b=[b[1],..,b[n]]
and c=[c[1],..,c[n]]
are the
exact weights and abscissae of the Gauss-Tschebyscheff quadrature rule,
respectively.
The function uses option
remember
. It is not sensitive to the environment variable
DIGITS
.
numeric::gldata
,
numeric::ncdata
,
numeric::quadrature
b[i]= PI/2/n*sin((2*i-1)*PI/2/n), c[i]=(1+cos((2*i-1)*PI/2/n))/2.
The following call produces exact data for the quadrature rule with two nodes:
>> numeric::gtdata(2)
-- -- 1/2 1/2 -- -- 1/2 1/2 -- -- | | PI 2 PI 2 | | 2 2 | | | | -------, ------- |, | ---- + 1/2, 1/2 - ---- | | -- -- 8 8 -- -- 4 4 -- --
numeric::quadrature
calls
numeric::gtdata
to provide the data for
Gauss-Tschebyscheff quadrature.