Computation of rational interpolants with prescribed poles
type: Item
instance of: scholarly article
title: Computation of rational interpolants with prescribed poles
zbMATH Open document ID: 0682.65001
DOI: 10.1016/0377-0427(89)90302-6
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The paper deals with the rational interpolant \(R_{M,N}\), \(M\geq 0\), \(N\geq 0\), belonging to the set of rational functions \({\mathcal R}_{M,N}\) and having N prescribed poles. A constructive proof for the existence and uniqueness of \(R_{M,N}\) that interpolates \(M+1\) Hermite data is given. It is based on explicit computation of the Cauchy-Vandermonde determinant in terms of nodes and poles. The proof constitutes the basis for the derivation of an algorithm computing the interpolant numerically. The computation scheme is described.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 4117727
zbMATH Keywords: rational interpolation
zbMATH Keywords: prescribed poles
zbMATH Keywords: Hermite data
zbMATH Keywords: Cauchy- Vandermonde determinant
zbMATH Keywords: algorithm
author: M. Gasca
author: José-Javier Martínez
author: Günter W. Mühlbach
reviewed by: Carmen Simerská
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90302-6
OpenAlex ID: W2064898684
cites work: The mühlbach-neville-aitken algorithm and some extensions
cites work: On Lagrange and Hermite interpolation in \(R^ k\).
cites work: Q4114254
cites work: A generalization of Sylvester's identity on determinants and some applications
cites work: Linear extrapolation by rational functions, exponentials and logarithmic functions
cites work: Q3266531
cites work: Q3770967
cites work: Q3292706
description: scientific article; zbMATH DE number 4117727