A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions
Author(s)
Townsend, Alex John
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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.
Date issued
2015-08Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
0036-1429
1095-7170