Tensorized block rational Krylov methods for tensor Sylvester equations - ArXiv:2306.007

Title: Tensorized block rational Krylov methods for tensor Sylvester equations

Authors: Angelo Alberto Casulli

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.