Adaptive low-rank approximation of collocation matrices

Authors:
M. Bebendorf;S. Rjasanow
Affiliations:
Max-Planck-Institute for Mathematics in the Sciences Inselstraße 22-26, 04103 Leipzig, Germany;Fachrichtung 6.1 - Mathematik, Universität des Saarlandes, 'Postfach 151150, 66041 Saarbrücken, Germany
Venue:
Computing
Year:
2003

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Abstract

This article deals with the solution of integral equations using collocation methods with almost linear complexity. Methods such as fast multipole, panel clustering and H-matrix methods gain their efficiency from approximating the kernel function. The proposed algorithm which uses the H-matrix format, in contrast, is purely algebraic and relies on a small part of the collocation matrix for its blockwise approximation by low-rank matrices. Furthermore, a new algorithm for matrix partitioning that significantly reduces the number of blocks generated is presented.