Projection methods for large Lyapunov matrix equations
type: Item
instance of: scholarly article
title: Projection methods for large Lyapunov matrix equations
zbMATH Open document ID: 1094.65039
author: Khalide Jbilou
author: A. J. Riquet
published in: Linear Algebra and its Applications
publication date: 2006-05-29T00:00:00Z
review text: Krylov subspace methods are proposed for solving large Lyapunov matrix algebraic equations of the form \(AX + XA^T + BB^T = 0\) where \(A\) and \(B\) are real \(n \times n\) and \(n \times s\) matrices, respectively, with \(s << n\). Equations of this kind appear in many problems of control theory such as computation of the Hankel singular values, model reduction and solution of matrix Riccati equations. The methods proposed are based on the Arnoldi process. It is shown how to extract low rank approximate solutions to Lyapunov equations and expressions are derived for the backward error. Two numerical experiments involving solutions of large Lyapunov equations are presented. There is no discussion on the connection between the numerical properties of the methods proposed and the conditioning of the Lyapunov equations solved.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5028754
zbMATH Keywords: global Arnoldi method
zbMATH Keywords: Krylov subspace methods
zbMATH Keywords: large Lyapunov matrix algebraic equations
zbMATH Keywords: Hankel singular values
zbMATH Keywords: model reduction
zbMATH Keywords: matrix Riccati equations
zbMATH Keywords: low rank approximate solutions
zbMATH Keywords: numerical experiments
reviewed by: Petko Hr. Petkov
describes a project that uses: Algorithm 432
MaRDI profile type: Publication
full work available at URL: j.laa.2004.11.004
OpenAlex ID: W1980292186
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DOI: 10.1016/J.LAA.2004.11.004
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description: scientific article