Name
Title | ||
|---|---|---|
Sparse approximation of multilinear problems with applications to kernel-based methods in UQ. |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s00211-017-0932-4 | Numerische Mathematik |
Keywords | Field | DocType |
41A05, 41A25, 41A63, 65B99, 65C05, 65D10, 65D32 | Kernel (linear algebra),Convergence (routing),Mathematical optimization,Uncertainty quantification,Sparse approximation,Approximations of π,Algorithm,Parametric statistics,Partial differential equation,Multilinear map,Mathematics | Journal |
Volume | Issue | ISSN |
139 | 1 | 0029-599X |
Citations | PageRank | References |
0 | 0.34 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fabio Nobile | 1 | 336 | 29.63 |
| Raul | 2 | 477 | 54.12 |
| Sören Wolfers | 3 | 0 | 0.34 |