A united approach to accelerating trigonometric expansions
type: Item
instance of: scholarly article
title: A united approach to accelerating trigonometric expansions
zbMATH Open document ID: 0852.41016
DOI: 10.1016/0898-1221(95)00084-4
author: Günter Baszenski
author: Manfred Tasche
author: Franz-Jürgen Delvos
publication date: 1995-12-18T00:00:00Z
review text: The problem of the approximation of smooth functions on a compact interval by algebraic polynomials in the maximum norm is studied. The Fourier series of such functions has slow convergence due to the fact that the periodic extension has jumps at the interval endpoints. The acceleration of convergence attains with the help of some well-known methods under various symmetry conditions on the functions. The authors present a unified derivation of these accelerating methods by using only the Euler representation of a smooth function. There are given explicit integral remainder representations in terms of the Bernoulli functions for all types of acceleration methods. Simultaneous error estimates for these methods are obtained.
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 826954
zbMATH Keywords: simultaneous approximation
zbMATH Keywords: convergence acceleration
zbMATH Keywords: periodic functions
zbMATH Keywords: Fourier series
reviewed by: D. K. Ugulava
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00084-4
OpenAlex ID: W1997292576
cites work: Q5546978
cites work: Accelerating convergence of trigonometric approximations
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cites work: Accelerating Convergence of Eigenfunction Expansions
cites work: Zur Konvergenzbeschleunigung von Fourier-Reihen
cites work: Error Estimates for Sine Series Expansions
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cites work: Q3995190
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 826954