Approximate solution of large sparse Lyapunov equations

Author

Gudmundsson, Thorkell ; Laub, Alan J.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

39

Issue

5

fYear

1994

fDate

5/1/1994 12:00:00 AM

Firstpage

1110

Lastpage

1114

Abstract

Describes a simple method for efficiently estimating the dominant eigenvalues and eigenvectors of the solution to a Lyapunov equation, without first solving the equation explicitly. The method is based on the power method and matrix-vector multiplications and is particularly suitable for problems where those multiplications can be done efficiently, such as where the coefficient matrices are large and sparse or low-rank. The same idea is directly applicable to balanced-truncation order reduction of linear systems

Keywords

Lyapunov methods; eigenvalues and eigenfunctions; linear systems; matrix algebra; Lyapunov equation; approximate solution; balanced-truncation order reduction; coefficient matrices; dominant eigenvalues; eigenvectors; large sparse Lyapunov equations; linear systems; matrix-vector multiplications; power method; Convergence; Iterative algorithms; Least squares approximation; Least squares methods; Linear systems; Nonlinear equations; Riccati equations; Sparse matrices; Stochastic processes; System identification;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.284905

Filename

284905