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dc.contributor.authorNobile, Fabio
dc.contributor.authorTempone, Raul
dc.contributor.authorWolfers, Sören
dc.date.accessioned2017-11-20T12:48:14Z
dc.date.available2017-11-20T12:48:14Z
dc.date.issued2017-11-16
dc.identifier.citationNobile F, Tempone R, Wolfers S (2017) Sparse approximation of multilinear problems with applications to kernel-based methods in UQ. Numerische Mathematik. Available: http://dx.doi.org/10.1007/s00211-017-0932-4.
dc.identifier.issn0029-599X
dc.identifier.issn0945-3245
dc.identifier.doi10.1007/s00211-017-0932-4
dc.identifier.urihttp://hdl.handle.net/10754/626181
dc.description.abstractWe provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.
dc.description.sponsorshipS. Wolfers and R. Tempone are members of the KAUST Strategic Research Initiative, Center for Uncertainty Quantification in Computational Sciences and Engineering. R. Tempone received support from the KAUST CRG3 Award Ref: 2281. F. Nobile received support from the Center for ADvanced MOdeling Science (CADMOS). We thank Abdul-Lateef Haji-Ali for many helpful discussions.
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/article/10.1007/s00211-017-0932-4
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s00211-017-0932-4
dc.titleSparse approximation of multilinear problems with applications to kernel-based methods in UQ
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalNumerische Mathematik
dc.eprint.versionPost-print
dc.contributor.institutionMATHICSE-CSQI, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
dc.identifier.arxivid1609.00246
kaust.personTempone, Raul
kaust.personWolfers, Sören
kaust.grant.number2281
refterms.dateFOA2018-11-16T00:00:00Z
dc.date.published-online2017-11-16
dc.date.published-print2018-05


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