An averaging method for the Fourier approximation to discontinuous functions
type: Item
instance of: scholarly article
title: An averaging method for the Fourier approximation to discontinuous functions
zbMATH Open document ID: 1113.65126
author: B. I. Yun
author: Kyung Soo Rim
author: Hyun-Chul Kim
published in: Applied Mathematics and Computation
publication date: 2007-02-13T00:00:00Z
review text: Both the truncated Fourier integral and the truncated Fourier series approximations for a discontinuous function bring about the inevitable oscillating error, say, the Gibbs phenomenon. Most basic filtering methods for the Gibbs phenomenon like the Féjer averaging method and the Lanczos averaging method have a disadvantage that the rise time is very slow even though the filtering effect is prominent away from the discontinuity. In this paper, a new averaging method of polynomial type which improves the rise time of the existing method is proposed. The present method can be regarded as a generalization of the traditional Lanczos averaging method. By several numerical examples, the efficiency of the present method is shown.
reviewed by: Feng Qi
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 5125218
zbMATH Keywords: truncated Fourier integral
zbMATH Keywords: truncated Fourier series
zbMATH Keywords: inevitable oscillating error
zbMATH Keywords: Gibbs phenomenon
zbMATH Keywords: filtering method
zbMATH Keywords: averaging method of polynomial type
zbMATH Keywords: Lanczos averaging method
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.amc.2006.05.060
OpenAlex ID: W2029866843
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DOI: 10.1016/J.AMC.2006.05.060
description: scientific article; zbMATH DE number 5125218