Articolo in rivista, 2020, ENG, 10.1016/j.laa.2020.06.013
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
Infinite matrices, Matrix equations, Rational Krylov subspaces, Stein equations, Sylvester equations, Toeplitz matrices
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 links
OAI-PMH: Dublin Core
OAI-PMH: Mods
OAI-PMH: RDF
DOI: 10.1016/j.laa.2020.06.013
URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379520303049
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