Abstract
In this paper, we propose a new projection method based on global Arnoldi algorithm for solving large Sylvester matrix equations A X + X B + C D T = 0 and the large generalized Sylvester matrix equations of the form A X B + X + C D 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.
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