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 Open image in new window (log(ɛ)2) tensor product vectors where ɛ is the relative approximation error. Numerical examples for systems of size 1024256 indicate that this method is suitable for high-dimensional problems.
KeywordsData-sparse approximation Sylvester equation low rank approximation Kronecker product high-dimensional problems
AMS Subject Classification65F05 65F30 65F50
Unable to display preview. Download preview PDF.