Discrete-time Lyapunov stability of large matrices
type: Item
instance of: scholarly article
title: Discrete-time Lyapunov stability of large matrices
zbMATH Open document ID: 0963.93054
DOI: 10.1016/S0377-0427(99)00185-5
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 2000-03-23T00:00:00Z
review text: Some techniques for analyzing the discrete-time stability of large matrices are proposed. These techniques combine Lyapunov theory and Krylov subspace methods. All the proposed methods need the computation of an approximate invariant subspace. Any good large eigensolver can be used for this step. The idea of the methods is to decompose the matrix into two blocks: a small block, obtained by Krylov-type methods, on which the classical discrete Lyapunov theory is applied and a large block whose either norm or its numerical radius is estimated. Using these two informations and some perturbation theory, one can justify mathematically the stability/instability of the matrix. Several numerical examples illustrate the behavior of the proposed method.
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93A15
zbMATH DE Number: 1423338
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: discrete-time stability
zbMATH Keywords: large matrices
zbMATH Keywords: Krylov subspace methods
reviewed by: Bozhidar Cheshankov
describes a project that uses: Harwell-Boeing sparse matrix collection
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00185-5
OpenAlex ID: W1971861408
description: scientific article; zbMATH DE number 1423338