An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments

DOI10.1007/s10444-018-9613-9zbMath1418.65037arXiv1705.07820OpenAlexW2618046004MaRDI QIDQ2631984

James Bremer

Publication date: 16 May 2019

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.07820

zbMATH Keywords

fast algorithmsspecial functionsRiccati equationBessel functionsChebyshev nodesChebyshev interpolationCarleson theoremspectral integrationKummer's equationChebyshev gridnonoscillatory phase functionsbivariate Chebyshev expansionDebye's asymptotic expansionnonoscillatory phase functionunivariate Chebyshev series expansion

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Asymptotic expansions of solutions to ordinary differential equations (34E05) Numerical approximation and evaluation of special functions (33F05) Numerical methods for ordinary differential equations (65L99) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (6)

On computation of the Bessel function by summing up the series ⋮ Analysis of multivariate Gegenbauer approximation in the hypercube ⋮ Interpolative Decomposition Butterfly Factorization ⋮ A unified framework for oscillatory integral transforms: when to use NUFFT or butterfly factorization? ⋮ A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces ⋮ BesselEval

Uses Software

• mctoolbox
• DLMF
• Algorithm 644

Cites Work

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• An algorithm for the rapid evaluation of special function transforms
• On the asymptotics of Bessel functions in the Fresnel regime
• On convergence and growth of partial sums of Fourier series
• On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations
• Fast Computation of Fourier Integral Operators
• A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
• Algorithm 644
• Accuracy and Stability of Numerical Algorithms
• Butterfly Factorization
• Numerical Methods for Special Functions
• On the convergence of multiple Fourier series
• Interpolative Butterfly Factorization
• ON THE CHOICE OF STANDARD SOLUTIONS FOR A HOMOGENEOUS LINEAR DIFFERENTIAL EQUATION OF THE SECOND ORDER

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