Reduction of the Gibbs phenomenon for smooth functions with jumps by the \(\varepsilon \)-algorithm
type: Item
instance of: scholarly article
title: Reduction of the Gibbs phenomenon for smooth functions with jumps by the \(\varepsilon \)-algorithm
zbMATH Open document ID: 1165.65087
author: Bernhard Beckermann
author: Ana C. Matos
author: F. Wielonsky
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-08T00:00:00Z
review text: For smoothing the Gibbs phenomenon, \textit{C. Brezinski} [Numer. Algorithms 36, 309--324 (2004; Zbl 1071.42003)] proposed a procedure based on Padé approximation of the analytic function \(G_n(f)(z)\), \(z=e^{it}\), \(-\pi \leq t \leq \pi\), the real part of which is the truncated Fourier series of the unknown function \(f\). The aim of the paper is to provide error estimates for some model functions \(f\), possibly peturbed by a sufficiently smooth function.
reviewed by: Winfried Sickel
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 5309299
zbMATH Keywords: Fourier series
zbMATH Keywords: Gibbs phenomenon
zbMATH Keywords: convergence acceleration
zbMATH Keywords: \(\varepsilon\)-algorithm
zbMATH Keywords: Padé-Fourier approximants
zbMATH Keywords: Padé-Chebyshev approximants
zbMATH Keywords: hypergeometric functions
MaRDI profile type: Publication
full work available at URL: j.cam.2007.11.011
OpenAlex ID: W2101639249
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DOI: 10.1016/J.CAM.2007.11.011
description: scientific article; zbMATH DE number 5309299