A new projection method for solving large Sylvester equations

Authors:
Liang Bao;Yiqin Lin;Yimin Wei
Affiliations:
Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Educ ...;Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou, 425006, PR China;Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Educ ...
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

In this paper, we propose a new projection method based on global Arnoldi algorithm for solving large Sylvester matrix equations AX+XB+CD^T=0 and the large generalized Sylvester matrix equations of the form AXB+X+CD^T=0. We show how to extract low-rank approximate solutions to Sylvester matrix equations and generalized Sylvester matrix equations. Some theoretical results are given. Numerical tests report the effectiveness of these methods.