A note on adaptivity in factorized approximate inverse preconditioning

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dc.contributor.author Kopal, Jiří
dc.contributor.author Rozložník, Miroslav
dc.contributor.author Tůma, Miroslav
dc.date.accessioned 2020-10-16T06:06:27Z
dc.date.available 2020-10-16T06:06:27Z
dc.date.issued 2020
dc.identifier.uri https://dspace.tul.cz/handle/15240/157905
dc.identifier.uri https://content.sciendo.com/view/journals/auom/28/2/article-p149.xml
dc.description.abstract The problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram-Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix diagonalization in computation of electronic structures but approximating inverses is of an interest in parallel computations in general. Our approach uses adaptive dropping of the matrix entries with the control based on the computed intermediate quantities. Strategy has been introduced as a way to solve difficult application problems and it is motivated by recent theoretical results on the loss of orthogonality in the generalized Gram-Schmidt process. Nevertheless, there are more aspects of the approach that need to be better understood. The diagonal pivoting based on a rough estimation of condition numbers of leading principal submatrices can sometimes provide inefficient preconditioners. This short study proposes another type of pivoting, namely the pivoting that exploits incremental condition estimation based on monitoring both direct and inverse factors of the approximate factorization. Such pivoting remains rather cheap and it can provide in many cases more reliable preconditioner. Numerical examples from real-world problems, small enough to enable a full analysis, are used to illustrate the potential gains of the new approach. cs
dc.language.iso cs cs
dc.publisher OVIDIUS UNIV PRESS, FAC MATHEMATICS & COMPUTER SCIENCE, BULEVARDUL MAMAIA 124, CONSTANTA, 900527, ROMANIA
dc.relation.ispartof ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
dc.subject sparse approximate inverse preconditioners cs
dc.subject approximate factorization cs
dc.subject generalized Gram-Schmidt process cs
dc.title A note on adaptivity in factorized approximate inverse preconditioning cs
dc.identifier.doi 10.2478/auom-2020-0024
local.relation.volume 28
local.relation.issue 2
local.citation.spage 149
local.citation.epage 159
local.event.sdate 2018-10-24
local.event.edate 2018-10-28
local.event.title 12th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems
local.event.location Constanta, ROMANIA


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