Name
Abstract | ||
|---|---|---|
We consider linear systems $A(\alpha) x(\alpha) = b(\alpha)$ depending on possibly many parameters $\alpha = (\alpha_1,\ldots,\alpha_p)$. Solving these systems simultaneously for a standard discretization of the parameter range would require a computational effort growing drastically with the number of parameters. We show that a much lower computational effort can be achieved for sufficiently smooth parameter dependencies. For this purpose, computational methods are developed that benefit from the fact that $x(\alpha)$ can be well approximated by a tensor of low rank. In particular, low-rank tensor variants of short-recurrence Krylov subspace methods are presented. Numerical experiments for deterministic PDEs with parametrized coefficients and stochastic elliptic PDEs demonstrate the effectiveness of our approach. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/100799010 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
parametrized linear systems,low-rank tensor variant,stochastic elliptic pdes,computational method,computational effort,linear system,smooth parameter dependency,deterministic pdes,low-rank tensor krylov subspace,parameter range,lower computational effort,low rank,tensor,low rank approximation,singular value decomposition,interpolation,approximation,discretization,partial differential equations,tucker decomposition | Krylov subspace,Singular value decomposition,Discretization,Mathematical optimization,Tensor,Linear system,Mathematical analysis,Low-rank approximation,Tucker decomposition,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 4 | 0895-4798 |
Citations | PageRank | References |
40 | 1.65 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel Kressner | 1 | 449 | 48.01 |
| Christine Tobler | 2 | 108 | 5.61 |