Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform
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.
discrete Fourier transform on irregular grid
scientific article; zbMATH DE number 98365