We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.
J. R. Singler, "Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition," Proceedings of the 2008 American Control Conference, Institute of Electrical and Electronics Engineers (IEEE), Jun 2008.
The definitive version is available at http://dx.doi.org/10.1109/ACC.2008.4586502
2008 American Control Conference
Mathematics and Statistics
Keywords and Phrases
Lyapunov Methods; Approximation Theory; Infinite Dimensional Problems; Matrix Algebra; Matrix Approximations; Proper Orthogonal Decomposition
Article - Conference proceedings
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