XploRe Help : GaussLegendre

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	math
See also:	simpsonint

Quantlet:		GaussLegendre
Description:		abscissas and weights of the Gauss-Legendre n-point quadrature.

Usage:	`{X,W} = GaussLegendre(x1,x2,n,EPS)`
Input:
	`x1`	scalar, lower limit of integretion
	`x2`	scalar, upper limit of integration
	`n`	scalar, integer, number of points of integration
	`EPS`	scalar, relative prcision
Output:
	`X`	n x 1 vector of abscissas
	`W`	n x 1 vector of weights

Example:

y=GaussLegendre(0,20,3,0.00001) y

Result:

Contents of y.X
[1,]    2.254
[2,]       10
[3,]   17.746
Contents of y.W
[1,]   5.5556
[2,]   8.8889
[3,]   5.5556

Example:

library("math") y=GaussLegendre(-3,3,10,0.00001) ;calculate an integral on(-3,3) interval sum(pdfn(y.X).*y.W)

Result:

Contents of sum
[1,]   0.9973

Author: P. Uniejewski, R. Weron, 20040620 license MD*Tech