Tensorized block rational Krylov methods for tensor Sylvester equations

We introduce the definition of tensorized block rational Krylov subspaces and their relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in [2]. 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 and some strategies for poles selection based on the techniques developed in [1]. References [1] A. A. Casulli and L. Robol. “An effcient block rational Krylov solver for Sylvester equations with adaptive pole selection”. In: arXiv preprint arXiv:2301.08103 (2023). [2] D. Kressner and C. Tobler. “Krylov subspace methods for linear systems with tensor product structure”. In: SIAM Journal on Matrix Analysis and Applications 31.4 (2010), pp. 1688–1714