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Preconditioners for hierarchical matrices based on their extended sparse form
Daria Sushnikova, Ivan V. Oseledets
In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with $\mathc…
From low-rank approximation to an efficient rational Krylov subspace method for the Lyapunov equation
D. A. Kolesnikov, I. V. Oseledets
We propose a new method for the approximate solution of the Lyapunov equation with rank- right-hand side, which is based on extended rational Krylov subspace approximation with…
Time integration of tensor trains
Christian Lubich, Ivan Oseledets, Bart Vandereycken
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the proj…
Fast multidimensional convolution in low-rank formats via cross approximation
M. V. Rakhuba, I. V. Oseledets
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better com…