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Fast Computation of Singular Oscillatory Fourier Transforms
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-17
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We consider the problem of the numerical evaluation of singular oscillatory Fourier transforms ∫abx-aαb-xβf(x)eiωxdx, where α>-1 and β>-1.
Based on substituting the original interval of integration by the paths of steepest descent, if f is analytic in the complex region G containing [a, b], the computation of integrals can be transformed into the problems of integrating two integrals on [0, ∞) with the integrand that does not oscillate and decays exponentially fast, which can be efficiently computed by using the generalized Gauss Laguerre quadrature rule.
The efficiency and the validity of the method are demonstrated by both numerical experiments and theoretical results.
More importantly, the presented method in this paper is also a great improvement of a Filon-type method and a Clenshaw-Curtis-Filon-type method shown in Kang and Xiang (2011) and the Chebyshev expansions method proposed in Kang et al.
(2013), for computing the above integrals.
American Psychological Association (APA)
Kang, Hongchao& Shao, Xinping. 2014. Fast Computation of Singular Oscillatory Fourier Transforms. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1015208
Modern Language Association (MLA)
Kang, Hongchao& Shao, Xinping. Fast Computation of Singular Oscillatory Fourier Transforms. Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1015208
American Medical Association (AMA)
Kang, Hongchao& Shao, Xinping. Fast Computation of Singular Oscillatory Fourier Transforms. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1015208
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1015208