A Levin-type algorithm for accelerating the convergence of Fourier series
type: Item
instance of: scholarly article
title: A Levin-type algorithm for accelerating the convergence of Fourier series
zbMATH Open document ID: 0788.65141
DOI: 10.1007/BF02141933
author: Herbert H. H. Homeier
published in: Numerical Algorithms
publication date: 1994-05-30T00:00:00Z
review text: A nonlinear Levin-type algorithm is presented which is able to accelerate the convergence of Fourier series. The remainder is assumed to be the product of a remainder estimate and the sum of the first terms of two Poincaré-type expansions which are premultiplied by two different phase factors. This transformation is exact for Fourier series of the following type: \(\sum^ \infty_{n=0} q^ n (A\cos (nx)+ B\sin(nx))\) with \(0<| q|<1\). It is shown that this algorithm accelerates the convergence of Fourier series.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 65B10
zbMATH DE Number: 440289
zbMATH Keywords: acceleration of convergence
zbMATH Keywords: nonlinear Levin-type algorithm
zbMATH Keywords: Fourier series
zbMATH Keywords: Poincaré-type expansions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02141933
OpenAlex ID: W1990330235
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description: scientific article; zbMATH DE number 440289