On the stability of large matrices
type: Item
instance of: scholarly article
title: On the stability of large matrices
zbMATH Open document ID: 0943.15009
DOI: 10.1016/S0377-0427(98)00231-3
published in: Journal of Computational and Applied Mathematics
publication date: 1999-09-02T00:00:00Z
review text: The distance \(\text{rstab} (A)\) of a stable matrix \(A\) to the set of unstable matrices and the norm of the exponential of matrices constitute two important topics in stability theory. The method proposed partitions the matrix into two blocks; a small block in which the stability is studied and a large block whose field of values is located in the complex plane. Using the information on the blocks and some results on perturbation theory, the authors give sufficient conditions for the stability of the original matrix, a lower bound of \(\text{rstab}(A)\) and an upper bound on the norm of the exponential of \(A\). They illustrate these theoretical bounds on a practical test problem. The paper contains sections of introduction, on the stability of matrices, case of large matrices numerical experiments, and conclusion.
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1331066
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: stability radius
zbMATH Keywords: projection technique
zbMATH Keywords: exponential of matrices
zbMATH Keywords: stability theory
zbMATH Keywords: norm
zbMATH Keywords: numerical experiments
author: A. Malyshev
author: M. Sadkane
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
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full work available at URL: s0377-0427(98)00231-3
OpenAlex ID: W2158672051
description: scientific article; zbMATH DE number 1331066