A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics
The authors introduce a generalized fast multipole method that leads to an accelerated version of the filtering process. It is described as a set of modifications of the fast multipole method presented by \textit{L. Greengard} and \textit{V. Rokhlin} [J. Comput. Phys. 73, No. 2, 325-348 (1987; Zbl 0629.65005)] and by \textit{A. Dutt, M. Gu} and \textit{V. Rokhlin} [SIAM J. Numer. Anal. 33, No. 5, 1689-1711 (1996; Zbl 0862.65005)]. Furthermore, the authors describe an accelerated version of the algorithm presented by \textit{R. Jacob-Chien} and \textit{B. Alpert} [J. Comput. Phys. 136, No. 2, 580-584 (1997; Zbl 0885.65016)] in which two calls to the original one-dimensional fast multipole method are replaced by one call to the new generalized fast multipole method. The performance of the proposed algorithms is illustrated by several numerical examples.
scientific article; zbMATH DE number 1282764