Approximate inverse preconditioners for some large dense random electrostatic interaction matrices
Författare
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.
Avdelning/ar
- Matematik LTH
- Harmonic Analysis and Applications
Publiceringsår
2006
Språk
Engelska
Sidor
307-323
Publikation/Tidskrift/Serie
BIT Numerical Mathematics
Volym
46
Issue
2
Fulltext
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Springer
Ämne
- Mathematics
Nyckelord
- dense matrices
- preconditioners
- sparse approximate
- inverses
- potential theory
- iterative methods
- integral equations
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 0006-3835