Improving Fourier partial sum approximation for discontinuous functions using a weight function
type: Item
instance of: scholarly article
title: Improving Fourier partial sum approximation for discontinuous functions using a weight function
zbMATH Open document ID: 1470.42008
DOI: 10.1155/2017/1364914
author: B. I. Yun
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: We introduce a generalized sigmoidal transformation \(w_m(r; x)\) on a given interval \([a, b]\) with a threshold at \(x = r \in(a, b)\). Using \(w_m(r; x)\), we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 6929543
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1364914
OpenAlex ID: W2768811274
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description: scientific article; zbMATH DE number 6929543