, Volume 70, Issue 1, pp 1–24 | Cite as

Adaptive Low-Rank Approximation of Collocation Matrices

  • M. Bebendorf
  • S. Rjasanow

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.

AMS Subject Classification: 41A63, 41A80, 65D05, 65D15, 65F05, 65F30. 
Keywords: Integral equations, hierarchical matrices, low-rank approximation, fast solvers. 


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Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • M. Bebendorf
    • 1
  • S. Rjasanow
    • 2
  1. 1.Max-Planck-Institute for Mathematics in the Sciences Inselstraße 22–26 04103 Leipzig, Germany e-mail: bebendorf@mis.mpg.deDE
  2. 2.Fachrichtung 6.1 – Mathematik, Universität des Saarlandes `Postfach 151150 66041 Saarbrücken, Germany e-mail: rjasanow@num.uni-sb.deDE

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