## 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.

Original language | English (US) |
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Pages (from-to) | 818-829 |

Number of pages | 12 |

Journal | Computers and Mathematics with Applications |

Volume | 67 |

Issue number | 4 |

DOIs | |

State | Published - Mar 1 2014 |

## Keywords

- Low-rank tensor formats
- Stochastic Galerkin matrix
- Stochastic PDEs
- Tensor approximation
- Uncertainty quantification

## ASJC Scopus subject areas

- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics