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

Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, Hermann Matthies & Philipp Wähnert
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 smoothness of...
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