Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure

摘要

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 s is the relative approximation error. Numerical examples for systems of size 1024~(256) indicate that this method is suitable for high-dimensional problems.