Unattainable points in multivariate rational interpolation
type: Item
instance of: scholarly article
title: Unattainable points in multivariate rational interpolation
zbMATH Open document ID: 0774.41001
published in: Journal of Approximation Theory
publication date: 1993-06-29T00:00:00Z
full work available at URL: 5136.pdf
review text: The concept of unattainability arises in rational interpolation when one wants to find the interpolatory solution of \(t-p/q\) \((p,q\) polynomials) by solving the lineralized interpolation problem \(qf-p\) first; the univariate situation has been studied extensively by \textit{G. Claessens} [J. Approximation Theory 22, 150-160 (1978; Zbl 0386.41002)]. The authors extend one of the univariate results to the multivariate case (concerning the possible common factors of the minimal solution \(p\), \(q\) of the linearized problem) and show through very nice examples that other results can not be extended (concerning the `triangular' and `block- diagonal' structure of the pointsets in \(I-0.06\text{cm }N^ 2\) for which the irreducible form of the minimal rational interpolant is the same).
reviewed by: Marcel G. de Bruin
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 222123
zbMATH Keywords: rational interpolation
zbMATH Keywords: examples
author: Hassane Allouche
author: Annie Cuyt
MaRDI profile type: Publication
OpenAlex ID: W2035818364
DOI: 10.1006/JATH.1993.1013
description: scientific article; zbMATH DE number 222123