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Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform. (English) Zbl 0765.65022

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 J. Carrier, L. Greengard and 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.
Reviewer: M.Tasche (Rostock)

MSC:

65D20 Computation of special functions and constants, construction of tables
65T40 Numerical methods for trigonometric approximation and interpolation

Citations:

Zbl 0656.65004
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References:

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