Numerical solution of the Lyapunov equation by approximate power iteration
type: Item
instance of: scholarly article
title: Numerical solution of the Lyapunov equation by approximate power iteration
zbMATH Open document ID: 0848.65033
DOI: 10.1016/0024-3795(94)00155-3
author: A. Scottedward Hodel
author: Bruce Tenison
author: Kameshwar Poolla
published in: Linear Algebra and its Applications
publication date: 1996-10-07T00:00:00Z
review text: The numerical solution of the Lyapunov equation has been addressed for several decades. In some applications, one is frequently interested in computing only the dominant invariant subspace of the symmetric positive definite solution \(X\) rather than the matrix \(X\) itself. This paper presents an approximate power iteration algorithm to solve this problem. Numerical experiments indicate that, if the matrix \(X\) admits a good low-rank solution, then the solver proposed in this paper provides indeed an orthogonal basis of a subspace which closely approximates the dominant \(X\)-invariant subspaces of corresponding dimension. A convergence analysis is also presented.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 871267
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: dominant invariant subspace
zbMATH Keywords: power iteration algorithm
reviewed by: Liu Xinguo
describes a project that uses: Algorithm 432
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00155-3
OpenAlex ID: W2035387301
cites work: Q3917065
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description: scientific article; zbMATH DE number 871267