Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure
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- Grasedyck, L. Computing (2004) 72: 247. doi:10.1007/s00607-003-0037-z
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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(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.