The resolution of the Gibbs phenomenon for ``spliced'' functions in one and two dimensions
type: Item
instance of: scholarly article
title: The resolution of the Gibbs phenomenon for ``spliced'' functions in one and two dimensions
zbMATH Open document ID: 0911.65145
DOI: 10.1016/S0898-1221(97)00086-2
publication date: 1999-04-22T00:00:00Z
review text: Methods that eliminate the Gibbs phenomenon for analytic but non-periodic functions in one variable by employing the Gegenbauer polynomials [cf. \textit{D. Gottlieb, C.-W. Shu, A. Solomonoff} and \textit{H. Vandeven}, J. Comput. Appl. Math. 43, No. 1-2, 81-98 (1992; Zbl 0781.42022)] or the Bernoulli polynomials [cf. \textit{K. S. Eckhoff}, Math. Comput. 64, No. 210, 671-690 (1995; Zbl 0830.65144)] have been developed earlier. Extending these methods the authors provide here accurate reconstruction of ``spliced'' functions in full domain. For the bivariate case the authors prove exponential convergence of the Gegenbauer method.
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1067159
zbMATH Keywords: Gibbs phenomenon
zbMATH Keywords: Fourier series
zbMATH Keywords: Gegenbauer polynomials
zbMATH Keywords: Bernoulli polynomials
zbMATH Keywords: reconstruction of spliced functions
zbMATH Keywords: exponential convergence
author: Anne Gelb
author: D. Gottlieb
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1067159