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MiS Preprint
48/2003

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

Lars Grasedyck

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 ${\cal O}(\log(\varepsilon)^{2})$ tensor product vectors where $\varepsilon$ is the relative approximation error. Numerical examples for systems of size $1024^{256}$ indicate that this method is suitable for high-dimensional problems.

Received:
May 28, 2003
Published:
May 28, 2003
MSC Codes:
15A69, 65F05, 65N22
Keywords:
high-dimensional problems, kronecker product, low rank approximation

Related publications

inJournal
2004 Repository Open Access
Lars Grasedyck

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

In: Computing, 72 (2004) 3/4, pp. 247-265