Least-squares orthogonal polynomials
type: Item
instance of: scholarly article
title: Least-squares orthogonal polynomials
zbMATH Open document ID: 0774.65009
DOI: 10.1016/0377-0427(93)90298-P
author: Claude Brezinski
author: Ana C. Matos
published in: Journal of Computational and Applied Mathematics
publication date: 1993-11-17T00:00:00Z
review text: Let \(c\) be a linear functional defined on the space of complex polynomials. While orthogonal polynomials \(P_ k\) are defined by \(c(x^ i P_ k(x))=0\) for \(i=1,2,\dots,k-1\), the authors consider polynomials \(R_ k\) which minimize \(\sum_{i=0}^ m [c(x^ i R_ k(x))]^ 2\) and call them least squares orthogonal polynomials. A computation of the polynomials by a Lanczos-type process is considered. The authors discuss how a breakdown of the recursion can be avoided. An application deals with Padé-type approximation.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 219123
zbMATH Keywords: Padé approximation
zbMATH Keywords: Lanczos method
zbMATH Keywords: complex polynomials
zbMATH Keywords: least squares orthogonal polynomials
zbMATH Keywords: recursion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 219123