A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions

@article{Townsend2015AFA,
  title={A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions},
  author={Alex Townsend},
  journal={SIAM J. Numer. Anal.},
  year={2015},
  volume={53},
  pages={1897-1917}
}
  • Alex Townsend
  • Published 7 January 2015
  • Computer Science
  • SIAM J. Numer. Anal.
A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order $0$ as well as evaluating Schl\"{o}milch and Fourier--Bessel expansions in $\mathcal{O}(N(\log N)^2/\log\!\log N)$ 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… 

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