A new formal approach to the rational interpolation problem
type: Item
instance of: scholarly article
title: A new formal approach to the rational interpolation problem
zbMATH Open document ID: 0765.65016
DOI: 10.1007/BF01396222
author: Marc van Barel
author: Adhemar Bultheel
published in: Numerische Mathematik
publication date: 1993-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/133644
review text: The authors present a new algorithm for the construction of a rational function \(n(z)/d(z)\) satisfying the interpolation conditions \(n(z_ i)/d(z_ i)=l_ i/m_ i\), where \(z_ i\), \(i=1,2,\dots,p\), are the interpolation points and \(l_ i/m_ i\) the corresponding function values. This recursive algorithm does not require a recordering of the data points, thus allowing to add more interpolation data during the computation. Moreover, confluent interpolation points, poles and \(\infty\) may be considered as interpolation points. Not only the specific solution of the problem is given but also a parametrization of all solutions. A linear algebra interpretation of the problem shows that the algorithm can be used to handle a specific class of structured matrices.
reviewed by: Luigi Gatteschi
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 118302
zbMATH Keywords: rational interpolation
zbMATH Keywords: recursive algorithm
MaRDI profile type: Publication
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OpenAlex ID: W1976887220
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description: scientific article; zbMATH DE number 118302