A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions
Name
Townsend-2015-Fast analysis-based.pdf
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322.55 KB
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Adobe PDF
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Author(s)
Townsend, Alex John
Date Issued
August 2015
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Townsend, Alex. “A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions.” SIAM J. Numer. Anal. 53, no. 4 (January 2015): 1897–1917. © 2015, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order 0 as well as evaluating Schlömilch and Fourier--Bessel expansions in O(N(log N)[superscript 2]/loglog N) operations. The algorithm is based on an asymptotic expansion for Bessel functions of large arguments, the fast Fourier transform, and the Neumann addition formula. All the algorithmic parameters are selected from error bounds to achieve a near-optimal computational cost for any accuracy goal. Numerical results demonstrate the efficiency of the resulting algorithm.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/151003106
