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Article
Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition
Proceedings of the 2008 American Control Conference
  • John R. Singler, Missouri University of Science and Technology
Abstract

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.

Meeting Name
2008 American Control Conference
Department(s)
Mathematics and Statistics
Keywords and Phrases
  • Lyapunov Methods,
  • Approximation Theory,
  • Infinite Dimensional Problems,
  • Matrix Algebra,
  • Matrix Approximations,
  • Proper Orthogonal Decomposition
Document Type
Article - Conference proceedings
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2008 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
6-1-2008
Citation Information
John R. Singler. "Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition" Proceedings of the 2008 American Control Conference (2008)
Available at: http://works.bepress.com/john-singler/9/