On generating polynomials which are orthogonal over several intervals

Bernd Fischer; Gene H. Golub

doi:10.1090/S0025-5718-1991-1068818-5

On generating polynomials which are orthogonal over several intervals

Bernd Fischer^*, Gene H. Golub

^*Corresponding author for this work

Institute of Mathematics

Stanford University

12 Citations (Scopus)

Abstract

We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.

Original language	English
Journal	Mathematics of Computation
Volume	56
Issue number	194
Pages (from-to)	711-730
Number of pages	20
ISSN	0025-5718
DOIs	https://doi.org/10.1090/S0025-5718-1991-1068818-5
Publication status	Published - 01.01.1991

Access to Document

10.1090/S0025-5718-1991-1068818-5

Cite this

@article{0c91d15dd6324432925000d0b39dba85,

title = "On generating polynomials which are orthogonal over several intervals",

abstract = "We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.",

author = "Bernd Fischer and Golub, {Gene H.}",

year = "1991",

month = jan,

day = "1",

doi = "10.1090/S0025-5718-1991-1068818-5",

language = "English",

volume = "56",

pages = "711--730",

journal = "Mathematics of Computation",

issn = "0025-5718",

number = "194",

}

TY - JOUR

T1 - On generating polynomials which are orthogonal over several intervals

AU - Fischer, Bernd

AU - Golub, Gene H.

PY - 1991/1/1

Y1 - 1991/1/1

N2 - We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.

AB - We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.

UR - http://www.scopus.com/inward/record.url?scp=84966259408&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1991-1068818-5

DO - 10.1090/S0025-5718-1991-1068818-5

M3 - Journal articles

AN - SCOPUS:84966259408

SN - 0025-5718

VL - 56

SP - 711

EP - 730

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 194

ER -

On generating polynomials which are orthogonal over several intervals

Abstract

Access to Document

Other files and links

Fingerprint

Cite this