Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40520141001Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations10971117555ENF.Panjeh Ali BeikVali-Asr University of RafsanjanJournal Article20110725The 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.http://bims.iranjournals.ir/article_555_436d6ad5ed75e3a57eae6a19e45899b6.pdf