Computing

, Volume 72, Issue 3, pp 247–265

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

Article

DOI: 10.1007/s00607-003-0037-z

Cite this article as:
Grasedyck, L. Computing (2004) 72: 247. doi:10.1007/s00607-003-0037-z

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 https://static-content.springer.com/image/art%3A10.1007%2Fs00607-003-0037-z/MediaObjects/s00607-003-0037-zflb1.gif(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.

Keywords

Data-sparse approximationSylvester equationlow rank approximationKronecker producthigh-dimensional problems

AMS Subject Classification

65F0565F3065F50

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany