A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations

In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new approach projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in $A$ and $A^{-1}$. The reduced problem is then solved by me...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2007-01, Vol.29 (3), p.1268-1288
Main Author: Simoncini, V.
Format: Article
Language:English
Subjects:
Approximation
Control theory
Iterative methods
Methods
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Summary:In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new approach projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in $A$ and $A^{-1}$. The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the competitiveness of the new method, compared to a state-of-the-art approach based on the factorized alternating direction implicit iteration.
ISSN:1064-8275
1095-7197
DOI:10.1137/06066120X