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Approximate inverse preconditioners for some large dense random electrostatic interaction matrices

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Author

Summary, in English

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green's function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse.

Department/s

Publishing year

2006

Language

English

Pages

307-323

Publication/Series

BIT Numerical Mathematics

Volume

46

Issue

2

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • dense matrices
  • preconditioners
  • sparse approximate
  • inverses
  • potential theory
  • iterative methods
  • integral equations

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 0006-3835