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

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 phi(log(epsilon)(2)) tensor product vectors where E is the relative approximation error. Numerical examples for systems of size 1024(256) indicate that this method is suitable for high-dimensional problems.