DC FieldValueLanguage
dc.contributor.authorIske, Armin-
dc.contributor.authorLe Borne, Sabine-
dc.contributor.authorWende, Michael-
dc.date.accessioned2020-02-18T11:09:58Z-
dc.date.available2020-02-18T11:09:58Z-
dc.date.issued2017-10-03-
dc.identifier.citationSIAM Journal on Scientific Computing 39 (5): A2287-A2316 (2017)de_DE
dc.identifier.issn0196-5204de_DE
dc.identifier.urihttp://hdl.handle.net/11420/4954-
dc.description.abstractScattered data interpolation by radial kernel functions leads to linear equation systems with large, fully populated, ill-conditioned interpolation matrices. A successful iterative solution of such a system requires an efficient matrix-vector multiplication as well as an efficient preconditioner. While multipole approaches provide a fast matrix-vector multiplication, they avoid the explicit setup of the system matrix which hinders the construction of preconditioners, such as approximate inverses or factorizations which typically require the explicit system matrix for their construction. In this paper, we propose an approach that allows both an efficient matrix-vector multiplication as well as an explicit matrix representation which can then be used to construct a preconditioner. In particular, the interpolation matrix will be represented in hierarchical matrix format, and several approaches for the blockwise low-rank approximation are proposed and compared, of both analytical nature (separable expansions) and algebraic nature (adaptive cross approximation). The validity of using an approximate system matrix in the iterative solution of the interpolation equations is demonstrated through a range of numerical experiments.en
dc.language.isoende_DE
dc.relation.ispartofSIAM journal on scientific computingde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleHierarchical Matrix Approximation for Kernel-Based Scattered Data Interpolationde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishScattered data interpolation by radial kernel functions leads to linear equation systems with large, fully populated, ill-conditioned interpolation matrices. A successful iterative solution of such a system requires an efficient matrix-vector multiplication as well as an efficient preconditioner. While multipole approaches provide a fast matrix-vector multiplication, they avoid the explicit setup of the system matrix which hinders the construction of preconditioners, such as approximate inverses or factorizations which typically require the explicit system matrix for their construction. In this paper, we propose an approach that allows both an efficient matrix-vector multiplication as well as an explicit matrix representation which can then be used to construct a preconditioner. In particular, the interpolation matrix will be represented in hierarchical matrix format, and several approaches for the blockwise low-rank approximation are proposed and compared, of both analytical nature (separable expansions) and algebraic nature (adaptive cross approximation). The validity of using an approximate system matrix in the iterative solution of the interpolation equations is demonstrated through a range of numerical experiments.de_DE
tuhh.publisher.doi10.1137/16M1101167-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue5de_DE
tuhh.container.volume39de_DE
tuhh.container.startpageA2287de_DE
tuhh.container.endpageA2316de_DE
local.status.inpressfalsede_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextnone-
item.creatorOrcidIske, Armin-
item.creatorOrcidLe Borne, Sabine-
item.creatorOrcidWende, Michael-
item.mappedtypeArticle-
item.creatorGNDIske, Armin-
item.creatorGNDLe Borne, Sabine-
item.creatorGNDWende, Michael-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-4399-4442-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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