numeric::gtdata -- weights and
abscissae of Gauss-Tschebyscheff quadrature
Introductionnumeric::gtdata(n) returns the weights and
the abscissae of the Gauss-Tschebyscheff quadrature rule with
n nodes.
Call(s)numeric::gtdata(n)
Parametersn |
- | the number of nodes: a positive integer |
ReturnsA 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.
Side
EffectsThe function uses option
remember. It is not sensitive to the environment variable
DIGITS.
Related
Functionsnumeric::gldata,
numeric::ncdata,
numeric::quadrature
Detailsb[i]= PI/2/n*sin((2*i-1)*PI/2/n), c[i]=(1+cos((2*i-1)*PI/2/n))/2.
Example
1The 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 -- --
Backgroundnumeric::quadrature calls
numeric::gtdata to provide the data for
Gauss-Tschebyscheff quadrature.