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MiS Preprint
28/2012

Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats

Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, Hermann G. Matthies and Philipp Wähnert

Abstract

In this article we describe an efficient approximation of the stochastic Galerkin matrix which stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed to be a log-normal random field with given covariance and mean functions. The approximation is done in the canonical tensor format and then compared numerically with the tensor train and hierarchical tensor formats. It will be shown that under additional assumptions the approximation error depends only on the smoothness of the covariance function and does not depend either on the number of random variables nor the degree of the multivariate Hermite polynomials.

Received:
May 16, 2012
Published:
May 24, 2012
MSC Codes:
65N30, 35R60, 60H15, 15A69
Keywords:
tensor approximation, stochastic PDEs, Galerkin matrix, Tensor formats

Related publications

inJournal
2014 Repository Open Access
Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, Hermann G. Matthies and Philipp Wähnert

Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats

In: Computers and mathematics with applications, 67 (2014) 4, pp. 818-829