A note on adaptivity in factorized approximate inverse preconditioning

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dc.contributor.authorKopal, Jiří
dc.contributor.authorRozložník, Miroslav
dc.contributor.authorTůma, Miroslav
dc.date.accessioned2020-10-16T06:06:27Z
dc.date.available2020-10-16T06:06:27Z
dc.date.issued2020
dc.description.abstractThe 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.identifier.doi10.2478/auom-2020-0024
dc.identifier.urihttps://dspace.tul.cz/handle/15240/157905
dc.identifier.urihttps://content.sciendo.com/view/journals/auom/28/2/article-p149.xml
dc.language.isocscs
dc.publisherOVIDIUS UNIV PRESS, FAC MATHEMATICS & COMPUTER SCIENCE, BULEVARDUL MAMAIA 124, CONSTANTA, 900527, ROMANIA
dc.relation.ispartofANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
dc.subjectsparse approximate inverse preconditionerscs
dc.subjectapproximate factorizationcs
dc.subjectgeneralized Gram-Schmidt processcs
dc.titleA note on adaptivity in factorized approximate inverse preconditioningcs
local.citation.epage159
local.citation.spage149
local.event.edate2018-10-28
local.event.locationConstanta, ROMANIA
local.event.sdate2018-10-24
local.event.title12th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems
local.relation.issue2
local.relation.volume28
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