MathTL::GenMomentsPolynomial Class Reference

#include <ortho_poly.h>

Inheritance diagram for MathTL::GenMomentsPolynomial:

List of all members.

Public Member Functions
	GenMomentsPolynomial (const Array1D< double > &moments, const double a, const double b, const unsigned int N)
	GenMomentsPolynomial (const Array1D< double > &moments, const OrthogonalPolynomial &T, const double a, const double b, const unsigned int N)
double	a (const unsigned int k) const
double	b (const unsigned int k) const

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Detailed Description

orthogonal polynomials on [a,b] given by monomial or generalized moments of the weight function = ^b T_k(x)w(x)dx where the T_k also fulfill a three-term recursion; since we can only input a finite number of moments (2N), it is only possible to access a_1,...,a_N and b_1,...,b_N, so you should initialize with N as large as required for your purposes.

references: + Sack/Donovan: An Algorithm for Gaussian Quadrature given Modified Moments, Numer. Math. 18(1972), 465-478 + Golub/Gutknecht: Modified Moments for Indefinite Weight Functions, Numer. Math. 57(1990), 607-624 + Golub/Welsch: Calculation of Gauss quadrature rules, Math. Comp. 23(1969), 221-230

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Constructor & Destructor Documentation

MathTL::GenMomentsPolynomial::GenMomentsPolynomial	(	const Array1D< double > &	moments,
		const double	a,
		const double	b,
		const unsigned int	N
	)

Golub/Welsch algorithm: [GW]

Parameters:

moments	(at least) 2*N+1 monomial moments of the weight function
N	number of three-term recursion coefficients created

MathTL::GenMomentsPolynomial::GenMomentsPolynomial	(	const Array1D< double > &	moments,
		const OrthogonalPolynomial &	T,
		const double	a,
		const double	b,
		const unsigned int	N
	)

Sack/Donovan algorithm: 2(i),(ii) of [GG]

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Member Function Documentation

double MathTL::GenMomentsPolynomial::a

(

const unsigned int

k

)

const [virtual]

the coefficients a_k

Implements MathTL::OrthogonalPolynomial.

double MathTL::GenMomentsPolynomial::b

(

const unsigned int

k

)

const [virtual]

the coefficients b_k

Implements MathTL::OrthogonalPolynomial.

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The documentation for this class was generated from the following files:

• numerics/ortho_poly.h
• numerics/ortho_poly.cpp