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

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.
 [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:
Grant/Contract Number:
AC02-06CH11357; RG160236; DTRA-DMS 1322393
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 39; Journal Issue: 6; Journal ID: ISSN 1064-8275
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)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; convolution; fast Fourier transform; Fourier extension; Fredholm convolution integral; Toeplitz matrix; Volterra convolution integral
OSTI Identifier: