How to generate unknown orthogonal polynomials out of known orthogonal polynomials

Bernd Fischer; Gene H. Golub

doi:10.1016/0377-0427(92)90261-U

How to generate unknown orthogonal polynomials out of known orthogonal polynomials

Bernd Fischer^*, Gene H. Golub

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Mathematik

Stanford University

20 Zitate (Scopus)

Abstract

We consider the problem of generating the three-term recursion coefficients of orthogonal polynomials for a weight function v(t)=r(t)w(t), obtained by modifying a given weight function w by a rational function. Algorithms for the construction of the orthogonal polynomials for the new weight v in terms of those for the old weight w are presented. All the methods are based on modified moments. As applications we present Gaussian quadrature rules for integrals in which the integrant has singularities close to the interval of integration, and the generation of orthogonal polynomials for the (finite) Hermite weight e^-t², supported on a finite interval [-b, b].

Originalsprache	Englisch
Zeitschrift	Journal of Computational and Applied Mathematics
Jahrgang	43
Ausgabenummer	1-2
Seiten (von - bis)	99-115
Seitenumfang	17
ISSN	0377-0427
DOIs	https://doi.org/10.1016/0377-0427(92)90261-U
Publikationsstatus	Veröffentlicht - 25.11.1992

Fördermittel

Corrcsporhxx-to: Dr. B. Fischer, Institute of Applied h&hcmatics, University of Hamburg. W-2000 Hambtirg 13, Germany. * This author’s rcscarch was in part supported by the US Army under grant DAAI, 03-9L-G-0105. Part of this work was done while the first author was visiting the Departmento f Computer Science at the Stanford University. He would like to thank Gene Golub for his hospitality.

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AB - We consider the problem of generating the three-term recursion coefficients of orthogonal polynomials for a weight function v(t)=r(t)w(t), obtained by modifying a given weight function w by a rational function. Algorithms for the construction of the orthogonal polynomials for the new weight v in terms of those for the old weight w are presented. All the methods are based on modified moments. As applications we present Gaussian quadrature rules for integrals in which the integrant has singularities close to the interval of integration, and the generation of orthogonal polynomials for the (finite) Hermite weight e-t2, supported on a finite interval [-b, b].

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How to generate unknown orthogonal polynomials out of known orthogonal polynomials

Abstract

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