DC FieldValueLanguage
dc.contributor.authorLe Borne, Sabine-
dc.contributor.authorWende, Michael-
dc.date.accessioned2020-02-18T11:07:10Z-
dc.date.available2020-02-18T11:07:10Z-
dc.date.issued2020-01-07-
dc.identifier.citationNumerical Algorithms (2020-01-01)de_DE
dc.identifier.issn1017-1398de_DE
dc.identifier.urihttp://hdl.handle.net/11420/4953-
dc.description.abstractScattered data interpolation can be used to approximate a multivariate function by a linear combination of positive definite radial basis functions (RBFs). In practice, the approximation error stagnates (due to numerical instability) even if the function is smooth and the number of data centers is increased. A smaller approximation error can be obtained using multilevel interpolation on a sequence of nested subsets of the initial set of centers. For the construction of these nested subsets, we compare two thinning algorithms from the literature, a greedy algorithm based on nearest neighbor computations and a Poisson point process. The main novelty of our approach lies in the use of H-matrices both for the solution of linear systems and for the evaluation of residual errors at each level. For the solution of linear systems, we use GMRes combined with a domain decomposition preconditioner. Using H-matrices allows us to solve larger problems more efficiently compared with multilevel interpolation based on dense matrices. Numerical experiments with up to 50,000 scattered centers in two and three spatial dimensions demonstrate that the computational time required for the construction of the multilevel interpolant using H-matrices is of almost linear complexity with respect to the number of centers.en
dc.language.isoende_DE
dc.relation.ispartofNumerical Algorithmsde_DE
dc.subjectDomain decompositionde_DE
dc.subjectHierarchical matricesde_DE
dc.subjectMultilevel interpolationde_DE
dc.subjectPositive definitede_DE
dc.subjectPreconditioningde_DE
dc.subjectRadial basis functionde_DE
dc.subjectScattered data interpolationde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleMultilevel interpolation of scattered data using H -matricesde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishScattered data interpolation can be used to approximate a multivariate function by a linear combination of positive definite radial basis functions (RBFs). In practice, the approximation error stagnates (due to numerical instability) even if the function is smooth and the number of data centers is increased. A smaller approximation error can be obtained using multilevel interpolation on a sequence of nested subsets of the initial set of centers. For the construction of these nested subsets, we compare two thinning algorithms from the literature, a greedy algorithm based on nearest neighbor computations and a Poisson point process. The main novelty of our approach lies in the use of H-matrices both for the solution of linear systems and for the evaluation of residual errors at each level. For the solution of linear systems, we use GMRes combined with a domain decomposition preconditioner. Using H-matrices allows us to solve larger problems more efficiently compared with multilevel interpolation based on dense matrices. Numerical experiments with up to 50,000 scattered centers in two and three spatial dimensions demonstrate that the computational time required for the construction of the multilevel interpolant using H-matrices is of almost linear complexity with respect to the number of centers.de_DE
tuhh.publisher.doi10.1007/s11075-019-00860-1-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
dc.identifier.scopus2-s2.0-85077548793de_DE
local.status.inpressfalsede_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDLe Borne, Sabine-
item.creatorGNDWende, Michael-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidLe Borne, Sabine-
item.creatorOrcidWende, Michael-
item.languageiso639-1en-
item.mappedtypeArticle-
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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