A new projection method for solving large Sylvester equations

In this paper, we propose a new projection method based on global Arnoldi algorithm for solving large Sylvester matrix equations AX+XB+CDT=0 and the large generalized Sylvester matrix equations of the form AXB+X+CDT=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.