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Approximate inverse preconditioners for some large dense random electrostatic interaction matrices

Helsing, Johan LU (2006) In BIT Numerical Mathematics 46(2). p.307-323
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
dense matrices, preconditioners, sparse approximate, inverses, potential theory, iterative methods, integral equations
in
BIT Numerical Mathematics
volume
46
issue
2
pages
307 - 323
publisher
Springer
external identifiers
  • wos:000238444700005
  • scopus:33745316740
ISSN
0006-3835
DOI
10.1007/s10543-006-0057-0
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
5456708b-a0e1-4fd0-9d19-18d4a2f6dc9c (old id 405735)
alternative location
http://www.maths.lth.se/na/staff/helsing/BIT06.pdf
date added to LUP
2016-04-01 16:29:13
date last changed
2021-02-17 07:45:00
@article{5456708b-a0e1-4fd0-9d19-18d4a2f6dc9c,
  abstract     = {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.},
  author       = {Helsing, Johan},
  issn         = {0006-3835},
  language     = {eng},
  number       = {2},
  pages        = {307--323},
  publisher    = {Springer},
  series       = {BIT Numerical Mathematics},
  title        = {Approximate inverse preconditioners for some large dense random electrostatic interaction matrices},
  url          = {https://lup.lub.lu.se/search/files/4687302/3878572.pdf},
  doi          = {10.1007/s10543-006-0057-0},
  volume       = {46},
  year         = {2006},
}