A Nonuniform Fast Hankel Transform

Abstract. We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from [Formula: see text] nonuniform points to [Formula: see text] nonuniform frequencies in [Formula: see text] operations. Our approach combines local and asymptotic Bessel function expansions with nonuniform fast Fourier transforms. The order of each expansion is adjusted automatically according to error analysis to obtain any desired precision [Formula: see text]. Several numerical examples are provided which demonstrate the speed and accuracy of the algorithm in multiple regimes and applications. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/pbeckman/FastHankelTransform.jl and in the supplementary materials ( FastHankelTransform-jl-main.zip [21.4KB]). [Formula: see text]