Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure |
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Authors: | L Grasedyck |
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Affiliation: | (1) Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany |
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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 (log( )2) tensor product vectors where is the relative approximation error. Numerical examples for systems of size 1024256 indicate that this method is suitable for high-dimensional problems. |
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Keywords: | Data-sparse approximation Sylvester equation low rank approximation Kronecker product high-dimensional problems |
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