Theoretical results on the global GMRES method for solving generalized Sylvester matrix‎ ‎equations

Document Type: Research Paper

Author

Vali-Asr University of Rafsanjan

Abstract

‎The global generalized minimum residual (Gl-GMRES)‎
‎method is examined for solving the generalized Sylvester matrix equation‎
‎\[\sum\limits_{i = 1}^q {A_i } XB_i = C.\]‎
‎Some new theoretical results are elaborated for‎
‎the proposed method by employing the Schur complement‎.
‎These results can be exploited to establish new convergence properties‎
‎of the Gl-GMRES method for solving general (coupled) linear matrix‎
‎equations‎. ‎In addition‎, ‎the Gl-GMRES method for solving the generalized‎
‎Sylvester-transpose matrix equation is briefly studied‎.
‎Finally‎, ‎some numerical experiments are presented to illustrate‎
‎the efficiently of the Gl-GMRES method for solving the general‎
‎linear matrix equations‎.

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