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Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function.

Authors :
Yun, Beong In
Source :
Abstract & Applied Analysis. 11/22/2017, p1-7. 7p.
Publication Year :
2017

Abstract

We introduce a generalized sigmoidal transformation wm(r;x) on a given interval [a,b] with a threshold at x=r∈(a,b). Using wm(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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10853375
Database :
Academic Search Index
Journal :
Abstract & Applied Analysis
Publication Type :
Academic Journal
Accession number :
126396944
Full Text :
https://doi.org/10.1155/2017/1364914