A static class template for generating quadrature abcsissas and weights for arbitrary-order and rule in dimension 1. More...

#include <QuadratureRecursiveRelation.h>

Collaboration diagram for model::QuadratureRecursiveRelation:

Public Types
enum	{ dim =1 }

Static Public Member Functions
template<typename PolynomialType>
static Eigen::MatrixXd	abcsissasAndWeights (const int &qOrder)

Detailed Description

A static class template for generating quadrature abcsissas and weights for arbitrary-order and rule in dimension 1.

For a given quadrature rule (eg. Gauss-Legendre, Gauss-Chebyshev...), abscissas and weights can be coputed from the coefficients of the recursive relation that define the orthogonal polynomials of that rule. Recursive relations are in the form:

\[ P_n(x) = (A_n*x+B_n) * P_{n-1} - C_n * P_{n-2} \]

The actual coefficients \(A_n\), \(B_n\) and \(C_n\)

References:

[1] Golub, G.H., and Welsch, J.H. 1969, "Calculation of Gauss Quadrature Rules", Mathematics of Computation, vol. 23, pp. 221–230.
[2] Press, W. et al. "Numerical Recipes", 3rd edition, p.188.

Definition at line 42 of file QuadratureRecursiveRelation.h.