DC FieldValueLanguage
dc.contributor.authorKriemann, Ronald-
dc.contributor.authorLe Borne, Sabine-
dc.date.accessioned2020-02-19T07:25:40Z-
dc.date.available2020-02-19T07:25:40Z-
dc.date.issued2015-12-29-
dc.identifier.citationComputing and Visualization in Science 3 (17): 135-150 (2015-06-01)de_DE
dc.identifier.issn1432-9360de_DE
dc.identifier.urihttp://hdl.handle.net/11420/4968-
dc.description.abstractGiven a sparse matrix, its LU-factors, inverse and inverse factors typically suffer from substantial fill-in, leading to non-optimal complexities in their computation as well as their storage. In the past, several computationally efficient methods have been developed to compute approximations to these otherwise rather dense matrices. Many of these approaches are based on approximations through sparse matrices, leading to well-known ILU, sparse approximate inverse or factored sparse approximate inverse techniques and their variants. A different approximation approach is based on blockwise low rank approximations and is realized, for example, through hierarchical (š¯“—H-) matrices. While š¯“—H-inverses and š¯“—H-LU factors have been discussed in the literature, this paper will consider the construction of an approximation of the factored inverse through š¯“—H-matrices (š¯“—H-FAINV). We will describe a blockwise approach that permits to replace (exact) matrix arithmetic through approximate efficient š¯“—H-arithmetic. We conclude with numerical results in which we use approximate factored inverses as preconditioners in the iterative solution of the discretized convectionā€“diffusion problem.en
dc.language.isoende_DE
dc.relation.ispartofComputing and visualization in sciencede_DE
dc.subjectApproximate factored inversede_DE
dc.subjectHierarchical matricesde_DE
dc.subjectPreconditioningde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleH-FAINV: hierarchically factored approximate inverse preconditionersde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishGiven a sparse matrix, its LU-factors, inverse and inverse factors typically suffer from substantial fill-in, leading to non-optimal complexities in their computation as well as their storage. In the past, several computationally efficient methods have been developed to compute approximations to these otherwise rather dense matrices. Many of these approaches are based on approximations through sparse matrices, leading to well-known ILU, sparse approximate inverse or factored sparse approximate inverse techniques and their variants. A different approximation approach is based on blockwise low rank approximations and is realized, for example, through hierarchical (š¯“—H-) matrices. While š¯“—H-inverses and š¯“—H-LU factors have been discussed in the literature, this paper will consider the construction of an approximation of the factored inverse through š¯“—H-matrices (š¯“—H-FAINV). We will describe a blockwise approach that permits to replace (exact) matrix arithmetic through approximate efficient š¯“—H-arithmetic. We conclude with numerical results in which we use approximate factored inverses as preconditioners in the iterative solution of the discretized convectionā€“diffusion problem.de_DE
tuhh.publisher.doi10.1007/s00791-015-0254-y-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue3de_DE
tuhh.container.volume17de_DE
tuhh.container.startpage135de_DE
tuhh.container.endpage150de_DE
dc.identifier.scopus2-s2.0-84955752798-
local.status.inpressfalsede_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDKriemann, Ronald-
item.creatorGNDLe Borne, Sabine-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidKriemann, Ronald-
item.creatorOrcidLe Borne, Sabine-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-4399-4442-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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