Article ID Journal Published Year Pages File Type
4603892 Linear Algebra and its Applications 2006 15 Pages PDF
Abstract

In the present paper, we propose Krylov subspace methods for solving large Lyapunov matrix equations of the form AX + XAT + BBT = 0 where A and B are real n × n and n × s matrices, respectively, with s ≪ n. Such problems appear in many areas of control theory such as the computation of Hankel singular values, model reduction algorithms and others. The proposed methods are based on the Arnoldi process. We show how to extract low rank approximate solutions to Lyapunov matrix equations and give some theoretical results. Finally, some numerical tests will be reported to illustrate the effectiveness of the proposed method.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory