Journal article  Open Access

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

Robol L.

Rational Krylov subspaces  Geometry and Topology  FOS: Mathematics  15B05  Stein equations  Mathematics - Numerical Analysis  15A24  65F10  Algebra and Number Theory  Sylvester equations  Numerical Analysis  Matrix equations  Infinite matrices  Toeplitz matrices  Numerical Analysis (math.NA)  Discrete Mathematics and Combinatorics 

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.

Source: Linear algebra and its applications 604 (2020): 210–235. doi:10.1016/j.laa.2020.06.013

Publisher: North Holland [etc.], [New York], Stati Uniti d'America

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BibTeX entry
	title = {Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations},
	author = {Robol L.},
	publisher = {North Holland [etc.], [New York], Stati Uniti d'America},
	doi = {10.1016/j.laa.2020.06.013 and 10.48550/arxiv.1907.02753},
	journal = {Linear algebra and its applications},
	volume = {604},
	pages = {210–235},
	year = {2020}