Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform
type: Item
instance of: scholarly article
title: Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform
zbMATH Open document ID: 0765.65022
DOI: 10.1016/0021-9991(92)90333-T
author: John P. Boyd
published in: Journal of Computational Physics
publication date: 1993-01-17T00:00:00Z
review text: The author sketches the basic idea and some applications of the fast multipole method (FMM) for computing of \(\sum_{j=1}^ N a_ j/(x-x_ j)\) [see \textit{J. Carrier}, \textit{L. Greengard} and \textit{V. Rokhlin}, SIAM J. Sci. Stat. Comput. 9, No. 4, 669-689 (1988; Zbl 0656.65004)]. The FMM succeeds where the fast Fourier transform fails. The FMM can be used to evaluate Fourier or Chebyshev series on an irregular grid and to expansions of sinc functions, spherical harmonics, Legendre polynomials or Hermite functions.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 98365
zbMATH Keywords: pseudospectral cardinal functions
zbMATH Keywords: multipole expansion
zbMATH Keywords: discrete Fourier transform on irregular grid
zbMATH Keywords: fast multipole method
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: Fourier or Chebyshev series
zbMATH Keywords: expansions of sinc functions
zbMATH Keywords: spherical harmonics
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: Hermite functions
reviewed by: Manfred Tasche
MaRDI profile type: Publication
cites work: Q3993205
cites work: Q4199478
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cites work: An introduction to the numerical analysis of spectral methods. (Transl. of report CEA-N-2278, dated 1981, of the French Atomic Energy Commission, titled `Analyse numérique des méthodes spectrales')
cites work: High-accuracy approximation techniques for analytic functions
cites work: Q3811780
cites work: A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid
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description: scientific article; zbMATH DE number 98365