Sparse approximation of multilinear problems with applications to kernel-based methods in UQ
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant Number
2281Date
2017-11-16Online Publication Date
2017-11-16Print Publication Date
2018-05Permanent link to this record
http://hdl.handle.net/10754/626181
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Show full item recordAbstract
We 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.Citation
Nobile 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.Sponsors
S. 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.Publisher
Springer NatureJournal
Numerische MathematikarXiv
1609.00246Additional Links
http://link.springer.com/article/10.1007/s00211-017-0932-4ae974a485f413a2113503eed53cd6c53
10.1007/s00211-017-0932-4