, Volume 72, Issue 3–4, pp 247–265 | Cite as

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

  • L. Grasedyck


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.


Data-sparse approximation Sylvester equation low rank approximation Kronecker product high-dimensional problems 

AMS Subject Classification

65F05 65F30 65F50 


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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

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

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