%0 Journal Article
%T Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Panjeh Ali Beik, F.
%D 2014
%\ 10/01/2014
%V 40
%N 5
%P 1097-1117
%! Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations
%K Linear matrix equation
%K Krylov subspace
%K global GMRES
%K Schur complement
%R
%X 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.
%U http://bims.iranjournals.ir/article_555_436d6ad5ed75e3a57eae6a19e45899b6.pdf