A matrix for determining lower complexity barycentric representations of rational interpolants
type: Item
instance of: scholarly article
title: A matrix for determining lower complexity barycentric representations of rational interpolants
zbMATH Open document ID: 0959.65016
DOI: 10.1023/A:1019180807534
author: Jean-Paul Berrut
published in: Numerical Algorithms
publication date: 2000-11-22T00:00:00Z
review text: Given \(N+1\) nodes \(x_0, x_1, \dots, x_N\) and corresponding values \(f_0, f_1, \dots, f_N\) of a function \(f\) the barycentric rational interpolant of \(f\) is defined by \[ r_N(x)=\frac{\sum_{k=0}^{N}(u_k/(x-x_k))f_k}{\sum_{k=0}^{N}(u_k/(x-x_k))}. \] To remove some numerical disadvantages in computing \(r_N\) the author suggests to diminish the number of interpolation nodes and to compute only \(r_M(x)\) with \(M<N\). He presents an algorithm for computing the weights \(u_k\) and discuss its efficiency with several examples.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 1534762
zbMATH Keywords: rational interpolation
zbMATH Keywords: numerical complexity and stability
zbMATH Keywords: numerical examples
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: a:1019180807534
OpenAlex ID: W1648501525
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description: scientific article; zbMATH DE number 1534762