Existence and Computation of a Low Kronecker-Rank Approximant to the Solution of a Tensor System with Tensor Right-Hand Side

Lars Grasedyck

Contact the author: Please use for correspondence this email.
Submission date: 28. May. 2003
Pages: 19
published in: Computing, 72 (2004) 3/4, p. 247-265 
DOI number (of the published article): 10.1007/s00607-003-0037-z
Bibtex
with the following different title: Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
MSC-Numbers: 15A69, 65F05, 65N22
Keywords and phrases: high-dimensional problems, kronecker product, low rank approximation
Download full preprint: PDF (224 kB), PS ziped (206 kB)

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 tensor product vectors where is the relative approximation error. Numerical examples for systems of size indicate that this method is suitable for high-dimensional problems.