Approximate inverse preconditioners for some large dense random electrostatic interaction matrices

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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.
Original languageEnglish
Pages (from-to)307-323
JournalBIT Numerical Mathematics
Issue number2
Publication statusPublished - 2006

Bibliographical note

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Subject classification (UKÄ)

  • Mathematics


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


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