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Title: A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

Abstract

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

Authors:
 [1];  [2];  [3]
  1. Univ. of Kent, Canterbury (United Kingdom). School of Mathematics, Statistics, and Actuarial Science
  2. Argonne National Lab. (ANL), Argonne, IL (United States). Mathematics and Computer Science Division
  3. Univ. of California, Davis, CA (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of California, Davis, CA (United States); Univ. of Kent, Canterbury (United Kingdom)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF); Royal Society (United Kingdom)
OSTI Identifier:
1427516
Grant/Contract Number:  
AC02-06CH11357; RG160236; DTRA-DMS 1322393
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 39; Journal Issue: 6; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; convolution; fast Fourier transform; Fourier extension; Fredholm convolution integral; Toeplitz matrix; Volterra convolution integral

Citation Formats

Xu, Kuan, Austin, Anthony P., and Wei, Ke. A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions. United States: N. p., 2017. Web. doi:10.1137/17M1114764.
Xu, Kuan, Austin, Anthony P., & Wei, Ke. A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions. United States. doi:10.1137/17M1114764.
Xu, Kuan, Austin, Anthony P., and Wei, Ke. Thu . "A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions". United States. doi:10.1137/17M1114764.
@article{osti_1427516,
title = {A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions},
author = {Xu, Kuan and Austin, Anthony P. and Wei, Ke},
abstractNote = {In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N)2), where N is the number of degrees of freedom used in each of the Fourier extensions.},
doi = {10.1137/17M1114764},
journal = {SIAM Journal on Scientific Computing},
number = 6,
volume = 39,
place = {United States},
year = {Thu Dec 21 00:00:00 EST 2017},
month = {Thu Dec 21 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on December 21, 2018
Publisher's Version of Record

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Cited by: 1 work
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