theoretical results on the global gmres method for solving generalized sylvester matrix‎ ‎equations

‎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.