Articolo in rivista, 2020, ENG, 10.1016/j.laa.2020.06.013

Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations

Robol L.

CNR-ISTI, Pisa, Italy and University of Pisa, Pisa, Italy

We consider a class of linear matrix equations involving semi-infinite matrices which have a quasi-Toeplitz structure. These equations arise in different settings, mostly connected with PDEs or the study of Markov chains such as random walks on bidimensional lattices. We present the theory justifying the existence of the solution in an appropriate Banach algebra which is computationally treatable, and we propose several methods for computing them. We show how to adapt the ADI iteration to this particular infinite dimensional setting, and how to construct rational Krylov methods. Convergence theory is discussed, and numerical experiments validate the proposed approaches.

Linear algebra and its applications 604 , pp. 210–235

Keywords

Infinite matrices, Matrix equations, Rational Krylov subspaces, Stein equations, Sylvester equations, Toeplitz matrices

CNR authors

Robol Leonardo

CNR institutes

ISTI – Istituto di scienza e tecnologie dell'informazione "Alessandro Faedo"

ID: 424808

Year: 2020

Type: Articolo in rivista

Creation: 2020-07-02 11:08:01.000

Last update: 2023-06-28 17:32:33.000

CNR authors

External IDs

CNR OAI-PMH: oai:it.cnr:prodotti:424808

DOI: 10.1016/j.laa.2020.06.013

Scopus: 2-s2.0-85086769630

ISI Web of Science (WOS): 000558087600009