On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients
type: Item
instance of: scholarly article
title: On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients
zbMATH Open document ID: 0773.65005
author: Andrew S. Clarke
author: Bernie D. Shizgal
published in: Journal of Computational Physics
publication date: 1993-05-16T00:00:00Z
review text: This interesting paper is devoted to the study of the generation of several sets of orthogonal polynomials that are useful in the solution of a number of physical problems. Recurrence relations involving the coefficients of the three-term recurrence relations of these polynomials are established and their numerical instability is then studied. Divergent asymptotic series for the recurrence coefficients are also obtained and these are subsequently used to establish accurate approximations.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 167058
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: recurrence relations
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: numerical instability
reviewed by: C. L. Koul
MaRDI profile type: Publication
full work available at URL: jcph.1993.1016
OpenAlex ID: W2038376377
DOI: 10.1006/JCPH.1993.1016
Recommended article: Asymptotics of orthogonal polynomials via recurrence relations
Recommended article: Asymptotics for orthogonal polynomials defined by a recurrence relation
Recommended article: On the computation of recurrence coefficients for univariate orthogonal polynomials
Recommended article: Q4454640
Recommended article: Orthogonal polynomials with asymptotically periodic recurrent coefficients
Recommended article: Asymptotics for orthogonal polynomials with regularly varying recurrence coefficients
Recommended article: Asymptotic properties of orthogonal polynomials from their recurrence formula. II
Recommended article: Asymptotic computation of classical orthogonal polynomials
Recommended article: Asymptotic properties of orthogonal polynomials from their recurrence formula. I
Recommended article: Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
description: scientific article; zbMATH DE number 167058