Approximate inverse preconditioners for some large dense random electrostatic interaction matrices
(2006) In BIT Numerical Mathematics 46(2). p.307323 Abstract
 A sparse meshneighbour 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 meshneighbour 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:
https://lup.lub.lu.se/record/405735
 author
 Helsing, Johan ^{LU}
 organization
 publishing date
 2006
 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
 00063835
 DOI
 10.1007/s1054300600570
 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
 5456708ba0e14fd09d1918d4a2f6dc9c (old id 405735)
 alternative location
 http://www.maths.lth.se/na/staff/helsing/BIT06.pdf
 date added to LUP
 20160401 16:29:13
 date last changed
 20220128 20:01:26
@article{5456708ba0e14fd09d1918d4a2f6dc9c, abstract = {{A sparse meshneighbour 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 = {{00063835}}, keywords = {{dense matrices; preconditioners; sparse approximate; inverses; potential theory; iterative methods; integral equations}}, language = {{eng}}, number = {{2}}, pages = {{307323}}, 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/s1054300600570}}, volume = {{46}}, year = {{2006}}, }