A note on classical Gauss-Radau and Gauss-Lobatto quadratures
type: Item
instance of: scholarly article
title: A note on classical Gauss-Radau and Gauss-Lobatto quadratures
zbMATH Open document ID: 1200.41035
published in: Applied Numerical Mathematics
publication date: 2010-06-21T00:00:00Z
review text: Let \(\int_a^b f(x)w(x)dx \approx w_0f(a)+\sum_{j=1}^N w_j f(x_j)+\delta w_{N+1}f(b)\) be the classical Gauss-Radau (\(\delta=0\)) or the Gauss-Lobatto (\(\delta=1\)) quadrature formulae. This note is devoted to study the connection between the boundary weight \(w_0\) associated with the fixed node \(x_0=a\) and weights \(w_j\) corresponding to interior nodes \(x_j\). Some general expressions for the weights of the Gauss-Radau quadrature are obtained in terms of the eigenvalues of the Sturm-Liouville problem associated to orthogonality. As an application of the former results, it is obtained a characterization of the Gauss-Radau quadrature in terms of a one-point rule.
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 5723990
zbMATH Keywords: numerical quadrature
zbMATH Keywords: Gauss-Radau quadrature
zbMATH Keywords: Gauss-Lobatto quadrature
zbMATH Keywords: Sturm-Liouville problem
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: quadrature coefficients
author: Bruno D. Welfert
reviewed by: J. Illán
describes a project that uses: RADAU
MaRDI profile type: Publication
full work available at URL: j.apnum.2010.03.006
OpenAlex ID: W2035900119
cites work: Gauss-Radau formulae for Jacobi and Laguerre weight functions
cites work: High-order Gauss-Lobatto formulae
cites work: Q5533688
cites work: The weights of classical Gauss-Radau quadratures with double end-point
DOI: 10.1016/J.APNUM.2010.03.006
description: scientific article; zbMATH DE number 5723990