Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation
type: Item
instance of: scholarly article
title: Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation
zbMATH Open document ID: 1171.41004
author: John P. Boyd
author: Fei Xu
published in: Applied Mathematics and Computation
publication date: 2009-04-30T00:00:00Z
review text: Consider the approximation of a given function analytic in \((-1,1)\) by a \(N\)th degree polynomial that is chosen to minimize the least squares error at \(P\) equidistant points in the interval \([-1,1]\). Numerical evidence is presented that indicates that the Runge phenomenon which is present in the case \(P = N+1\) can be weakened, but not completely eliminated, for \(P \gg N+1\).
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 5550285
zbMATH Keywords: interpolation
zbMATH Keywords: Chebyshev interpolation
zbMATH Keywords: least squares approximation
zbMATH Keywords: polynomial approximation
zbMATH Keywords: divergence
MaRDI profile type: Publication
full work available at URL: j.amc.2008.12.087
OpenAlex ID: W2089171658
cites work: Bounds for polynomials with a unit discrete norm
cites work: Q3848301
cites work: On the Runge Example
cites work: Two results on polynomial interpolation in equally spaced points
cites work: Q4004970
cites work: Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions
cites work: Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid
cites work: Q5268582
DOI: 10.1016/J.AMC.2008.12.087
description: scientific article; zbMATH DE number 5550285