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.
- Lyapunov Methods,
- Approximation Theory,
- Infinite Dimensional Problems,
- Matrix Algebra,
- Matrix Approximations,
- Proper Orthogonal Decomposition
Available at: http://works.bepress.com/john-singler/9/