Fast and stable rational interpolation in roots of unity and Chebyshev points
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.41005
DOI: 10.1137/100797291
author: Ricardo Pachón
author: Pedro Gonnet
author: Joris Van Deun
published in: SIAM Journal on Numerical Analysis
publication date: 2012-08-23T00:00:00Z
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 6070637
zbMATH Keywords: rational interpolation
zbMATH Keywords: barycentric interpolation formula
zbMATH Keywords: discrete orthogonal polynomials
describes a project that uses: Algorithm 413
describes a project that uses: Chebfun
MaRDI profile type: Publication
OpenAlex ID: W1975959460
title: Fast and stable rational interpolation in roots of unity and Chebyshev points
review text: In recent years there has been increased interest in rational interpolant which is linear in the interpolated function when the denominator is prescribed see \textit{J.-P. Berrut}, [Comput. Math. Appl. 15, No. 1, 1--16 (1988; Zbl 0646.65006)]. The authors study here a novel solution of the Cauchy interpolation problem. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm presented is particularly simple. Motivation for studying such a problem is derived from the work in NEWLINE[\textit{L. N. Trefethen} et al. \texttt{Chebfun}. Version 4, software collection, (2011), \url{http://www.maths.ox.ac.uk/chebfun/ }]. The algorithms presented here are easy to implement in this system.
reviewed by: H. P. Dikshit
description: scientific article; zbMATH DE number 6070637