Computing the coefficients of a recurrence formula for numerical integration by moments and modified moments
type: Item
instance of: scholarly article
title: Computing the coefficients of a recurrence formula for numerical integration by moments and modified moments
zbMATH Open document ID: 0807.65016
DOI: 10.1016/0377-0427(93)90152-2
published in: Journal of Computational and Applied Mathematics
publication date: 1994-04-27T00:00:00Z
review text: The authors consider the evaluation of the class of integrals \(\int^ 1_{-1} e^{-\alpha x} f(x)dx\), where \(\alpha\) is a positive number and the function \(f\) is known only approximately on a discrete set of points. They use a Gaussian quadrature formula in which the nodes and weights have to be computed via a family of monic orthogonal polynomials with respect to the weight function through the three-term recurrence relation \[ P_{k+1}(x)= (x+ B_{k+1}) P_ k(x)- C_{k+1} P_{k-1}(x). \] The thrust of this paper is a careful evaluation of the coefficients to guarantee a good precision through a Mathematica program. A comparison between various methods, starting from moments and modified moments is shown. Numerical results are also presented.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 540466
zbMATH Keywords: numerical results
zbMATH Keywords: Gaussian quadrature formula
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: three-term recurrence relation
zbMATH Keywords: Mathematica program
zbMATH Keywords: comparison
zbMATH Keywords: moments
author: M. Morandi Cecchi
author: Michela Redivo-Zaglia
reviewed by: M. Zuhair Nashed
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: 0377-0427(93)90152-2
OpenAlex ID: W1971757387
cites work: Q3661894
cites work: Padé-type approximation and general orthogonal polynomials
cites work: Extrapolation methods
cites work: A new presentation of orthogonal polynomials with applications to their computation
cites work: Q3258508
cites work: Construction of Gauss-Christoffel Quadrature Formulas
cites work: On the Construction of Gaussian Quadrature Rules from Modified Moments
cites work: On Generating Orthogonal Polynomials
cites work: On the sensitivity of orthogonal polynomials to perturbations in the moments
cites work: Modified moments for indefinite weight functions
cites work: L'integrazione numerica di una classe di integralie utili nei calcoli quantomeccanici
cites work: Q4853665
cites work: An algorithm for Gaussian quadrature given modified moments
cites work: An Algorithm for the Inversion of Finite Hankel Matrices
cites work: Modified moments and Gaussian quadratures
cites work: Q3823708
description: scientific article; zbMATH DE number 540466