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Tensorized block rational Krylov methods for tensor Sylvester equations
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Abstract
We introduce the definition of tensorized block rational Krylov subspace and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in Kressner, D. & Tobler, C. (2010) Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl., 31,$1688$–$1714$. Moreover, we develop methods for the solution of tensor Sylvester equations with low multilinear or tensor train rank, based on projection onto a tensor block rational Krylov subspace. We provide a convergence analysis, some strategies for pole selection and techniques to efficiently compute the residual.
Title: Tensorized block rational Krylov methods for tensor Sylvester equations
Description:
Abstract
We introduce the definition of tensorized block rational Krylov subspace and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in Kressner, D.
& Tobler, C.
(2010) Krylov subspace methods for linear systems with tensor product structure.
SIAM J.
Matrix Anal.
Appl.
, 31,$1688$–$1714$.
Moreover, we develop methods for the solution of tensor Sylvester equations with low multilinear or tensor train rank, based on projection onto a tensor block rational Krylov subspace.
We provide a convergence analysis, some strategies for pole selection and techniques to efficiently compute the residual.
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