Tensorized block rational Krylov methods for tensor Sylvester equations

2023/06/01 by Angelo Casulli, Casulli, Angelo Alberto
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2306.00705

Abstract

We introduce the definition of tensorized block rational Krylov subspaces and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in [Kressner D., Tobler C., Krylov subspace methods for linear systems with tensor product structure, SIMAX, 2010]. 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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