An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series
type: Item
instance of: scholarly article
title: An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series
zbMATH Open document ID: 0914.65140
DOI: 10.1023/A:1019152928122
author: Herbert H. H. Homeier
published in: Numerical Algorithms
publication date: 1999-06-07T00:00:00Z
review text: The author studies the concept of hierarchical consistency in more detail. Its asymptotic variant is used to derive the I transformation. It is shown that the I transformation is a special case of the J transformation. The consequences of this fact are discussed. Also, some basic convergence theory for the I transformation is given. Several numerical examples are given which show that suitable variants of the I transformation are powerful nonlinear convergence accelerators for Fourier series with coefficients of monotonic behavior.
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 1234723
zbMATH Keywords: convergence acceleration
zbMATH Keywords: extrapolation
zbMATH Keywords: hierarchical consistency
zbMATH Keywords: numerical examples
zbMATH Keywords: Fourier series
zbMATH Keywords: iterative sequence transformation
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
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full work available at URL: a:1019152928122
OpenAlex ID: W1671293494
description: scientific article; zbMATH DE number 1234723