A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions

DOI10.1137/151003106zbMath1327.65271arXiv1501.01652OpenAlexW2963468398MaRDI QIDQ2945408

Alex Townsend

Publication date: 10 September 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.01652

zbMATH Keywords

Hankel transformfast Fourier transformasymptotic expansionsBessel functions

Mathematics Subject Classification ID

Numerical methods for integral transforms (65R10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (6)

Reducing dimensionality to model 2D rotating and standing waves in a delayed nonlinear optical system with thin annulus aperture ⋮ Fast discrete finite Hankel transform for equations in a thin annulus ⋮ Fast Expansion into Harmonics on the Disk: A Steerable Basis with Fast Radial Convolutions ⋮ Interpolative Decomposition Butterfly Factorization ⋮ Interpolative Butterfly Factorization ⋮ Computing with Functions in Spherical and Polar Geometries II. The Disk

Uses Software

• DLMF
• GitHub
• FastAsyTransforms

Cites Work

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• An algorithm for the rapid evaluation of special function transforms
• Algorithms to numerically evaluate the Hankel transform
• Fast algorithms for spherical harmonic expansions. II.
• An Algorithm for the Convolution of Legendre Series
• Dual algorithms for fast calculation of the Fourier-Bessel transform
• A Fast Algorithm for the Evaluation of Legendre Expansions
• Algorithm 644
• A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
• Fast Algorithms for Spherical Harmonic Expansions
• Bounds for Zeros of Some Special Functions

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