Gallivan, Kyle (Florida State Univ.), Van Dooren, Paul Michel (Univ. Catholique de Louvain), Vandendorpe, Antoine (Univ. Catholique de Louvain)

Model Reduction and the Solution of Sylvester Equations

Scheduled for presentation during the Mini-Symposium "Dimension reduction of large-scale systems I" (ThA05), Thursday, July 27, 2006, 11:40−12:05, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

Model reduction techniques are often required in computationally tractable algorithms for the solution of simulation, optimization, or control problems for large scale dynamical systems. For linear systems, essentially all reduced models can be produced using projection onto subspaces determined by the approximation constraints of the problem. For example, rational interpolation, e.g., Rational Krylov methods, and its generalization to tangential interpolation require projection onto so-called generalized Krylov subspaces whose bases solve a particular family of Sylvester equations. In this paper, we derive a numerically reliable way to compute an orthogonal basis of these generalized Krylov subspaces. The residual error of the large linear systems of equations that are solved in order to produce the bases are controlled so as to yield a small backward error in the associated Sylvester equations and in the model reduction problem. The efficiency and effectiveness of the algorithm is demonstrated for single and multipoint tangential interpolation examples.