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Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function
Author
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-22
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Yun, Beong In. 2017. Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function. Abstract and Applied Analysis،Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1120773
Modern Language Association (MLA)
Yun, Beong In. Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function. Abstract and Applied Analysis No. 2017 (2017), pp.1-7.
https://search.emarefa.net/detail/BIM-1120773
American Medical Association (AMA)
Yun, Beong In. Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function. Abstract and Applied Analysis. 2017. Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1120773
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1120773