Numerical solution and perturbation theory for generalized Lyapunov equations
type: Item
instance of: scholarly article
title: Numerical solution and perturbation theory for generalized Lyapunov equations
zbMATH Open document ID: 1003.65042
DOI: 10.1016/S0024-3795(02)00255-0
author: Tatjana Stykel
published in: Linear Algebra and its Applications
publication date: 2002-08-28T00:00:00Z
review text: The numerical solution and a perturbation theory for the generalized continuous-time Lyapunov equation \(E^*XA+ A^*XE= -G\) with a singular matrix \(E\) are presented. This equation may not have solutions and even if a solution exists, it is, in general, not unique. Generalizations of the Bartels-Stewart and Hammarling methods are proposed to compute a partial solution of the generalized Lyapunov equation with a special right-hand side. The numerical properties of these methods are discussed. A spectral condition number is introduced and perturbation bounds for the generalized Lyapunov equation are derived. Numerical examples are given.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 1790246
zbMATH Keywords: Bertels-Stewart method
zbMATH Keywords: numerical examples
zbMATH Keywords: generalized continuous-time Lyapunov equation
zbMATH Keywords: Hammarling methods
zbMATH Keywords: spectral condition number
zbMATH Keywords: perturbation bounds
reviewed by: Petko Hr. Petkov
describes a project that uses: SLICOT
describes a project that uses: mctoolbox
describes a project that uses: Algorithm 705
describes a project that uses: LAPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1790246