theoretical results on the global gmres method for solving generalized sylvester matrix equations
چکیده
the global generalized minimum residual (gl-gmres) method is examined for solving the generalized sylvester matrix equation [sumlimits_{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.