Orthogonal rational functions and quadrature on the real half line.
type: Item
instance of: scholarly article
title: Orthogonal rational functions and quadrature on the real half line.
zbMATH Open document ID: 1049.42012
DOI: 10.1016/S0885-064X(03)00002-5
author: Pablo González-Vera
author: Erik Hendriksen
author: Olav Njåstad
author: Adhemar Bultheel
published in: Journal of Complexity
publication date: 2003-08-19T00:00:00Z
review text: The notion of orthogonal Laurent polynomials is extended to orthogonal rational functions. The rational functions have prescribed poles which can be thought of as poles grouped around zero and infinity. The orthogonal rational functions give rise to quadrature rules of Gaussian flavour, and the weights of the \(n\)-point Gauss-type quadrature formula are given explicitly. Errors and convergence for these Gauss-type formulas is handled in detail. The connection is made with multipoint Padé approximation. The paper is somewhat strange in this particular journal since no complexity issues are considered.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1967204
zbMATH Keywords: orthogonal rational functions
zbMATH Keywords: orthogonal Laurent polynomials
zbMATH Keywords: Gauss quadrature
reviewed by: Walter Van Assche
describes a project that uses: GQRAT
MaRDI profile type: Publication
cites work: Q3235904
cites work: Generalized Gaussian quadrature formulas
cites work: Quadrature on the half line and two-point Padé approximants to Stieltjes functions. III: The unbounded case
cites work: Orthogonal rational functions and tridiagonal matrices
cites work: Q3848301
cites work: Polynômes orthogonaux formels - applications
cites work: Q4284658
cites work: Q3285751
cites work: Q3728580
cites work: Two-point Padé expansions for a family of analytic functions
cites work: A Strong Stieltjes Moment Problem
cites work: Q5534404
cites work: Q3847247
cites work: Q3660775
cites work: Another quadrature rule of highest algebraic degree of precision
cites work: Q5535928
cites work: Q5777281
cites work: Quadrature Formulas Based on Rational Interpolation
Recommended article: Orthogonal rational functions and quadrature on an interval
Recommended article: Quadrature and orthogonal rational functions
Recommended article: Orthogonal rational functions and quadrature on the unit circle
Recommended article: Q4840503
Recommended article: Orthogonal rational functions on the extended real line and analytic on the upper half plane
Recommended article: Orthogonal rational functions on a semi-infinite interval
Recommended article: Orthogonal rational functions on the real half line with poles in \([-\infty,0]\)
Recommended article: Q5457577
Recommended article: Q3069253
Recommended article: Q4223056
description: scientific article; zbMATH DE number 1967204