Hierarchical low-rank approximation of tensors by successive rank one corrections for preconditioning and solving high dimensional linear systems
Résumé
We propose an algorithm for preconditioning and solving high dimensional linear systems of equations in tensor format. The algorithm computes an approximation of a tensor in hierarchical Tucker format in a subspace constructed from successive rank one corrections. The algorithm can be applied for the approximation of a solution or of the inverse of an operator. In the latter case, properties such as sparsity or symmetry can be imposed to the approximation. The methodology is applied to high dimensional problems arising from the discretization of stochastic parametric problems.
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