Bi-orthogonality in rational approximation
type: Item
instance of: scholarly article
title: Bi-orthogonality in rational approximation
zbMATH Open document ID: 0627.41011
DOI: 10.1016/S0377-0427(87)80007-9
author: Arieh Iserles
author: E. B. Saff
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: It is well known that the Padé denominators of a Stieltjes series (a power series whose coefficients are the moments of a positive measure) are linked to orthogonal polynomials with respect to that measure. Rational interpolants of more general type are connected with orthogonal polynomials with respect to other measures. Here the authors show that simultaneous Padé approximants and Levin- Sidi approximants are connected with bi-orthogonal polynomials, polynomials \(p_ n\) which annihilate a collection of measures \(\phi_ m\). In this more general setting it is also sometimes possible to prove results on the zeros of the polynomials and convergence of approximants.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4019658
zbMATH Keywords: Stieltjes series
zbMATH Keywords: power series
reviewed by: Johan Karlsson
MaRDI profile type: Publication
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full work available at URL: s0377-0427(87)80007-9
OpenAlex ID: W2074003284
description: scientific article; zbMATH DE number 4019658