gaussquad

Construction of one-dimensional quadrature rules. More...

Functions
void	assemble_gauss (uint m, preal x, preal w)
	Construction of quadrature points and weights for Gaussian quadrature. More...

Detailed Description

Construction of one-dimensional quadrature rules.

Function Documentation

void assemble_gauss	(	uint	m,
		preal	x,
		preal	w
	)

Construction of quadrature points and weights for Gaussian quadrature.

The quadrature points are the zeros of the -th order Legendre polynomial. The Legendre polynomial can be expressed as the characteristic polynomial of a tridiagonal matrix, so its zeros can be computed by solving an eigenvalue problem. The quadrature weights can be obtained from the corresponding eigenvectors.

Parameters

m	Required number of quadrature points. The resulting quadrature rule will be exact for polynomials of order .
x	Should be an array of size , will be overwritten by the quadrature points in .
w	Should be an array of size , will be overwritten by the quadrature weights.