Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure

Authors:
L. Grasedyck
Affiliations:
Max-Planck-Institute for Mathematics in the Sciences, D Leipzig, Germany
Venue:
Computing
Year:
2004

Citing 6
Cited 7

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Abstract

In this paper we construct an approximation to the solution x of a linear system of equations Ax=b of tensor product structure as it typically arises for finite element and finite difference discretisations of partial differential operators on tensor grids. For a right-hand side b of tensor product structure we can prove that the solution x can be approximated by a sum of O(log(ε)2) tensor product vectors where ε is the relative approximation error. Numerical examples for systems of size 1024256 indicate that this method is suitable for high-dimensional problems.