Fast algorithms for spherical harmonic expansions, II
Journal of Computational Physics
The black-box fast multipole method
Journal of Computational Physics
Fast and accurate numerical methods for solving elliptic difference equations defined on lattices
Journal of Computational Physics
A Fourier-series-based kernel-independent fast multipole method
Journal of Computational Physics
Journal of Computational Physics
A Fast Randomized Algorithm for Computing a Hierarchically Semiseparable Representation of a Matrix
SIAM Journal on Matrix Analysis and Applications
An automatic learning system to derive multipole and local expansions for the fast multipole method
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
A fast BIE iteration method for an arbitrary body in a flow of incompressible inviscid fluid
Journal of Computational and Applied Mathematics
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
A fast solver for Poisson problems on infinite regular lattices
Journal of Computational and Applied Mathematics
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A version of the fast multipole method (FMM) is described for charge distributions on the line. Previously published schemes of this type relied either on analytical representations of the potentials to be evaluated (multipoles, Legendre expansions, Taylor series, etc.) or on tailored representations that were constructed numerically (using, e.g., the singular value decomposition (SVD), artificial charges, etc.). The algorithm of this paper belongs to the second category, utilizing the matrix compression scheme described in [H. Cheng, Z. Gimbutas, P. G. Martinsson, and V. Rokhlin, SIAM J. Sci. Comput. 26 (2005), pp. 1389-1404]. The resulting scheme exhibits substantial improvements in the CPU time requirements. Furthermore, the scheme is applicable to a wide variety of potentials; in this respect, it is similar to the SVD-based FMMs. The performance of the method is illustrated with several numerical examples.