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.
Panjeh Ali Beik, F. (2014). Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations. Bulletin of the Iranian Mathematical Society, 40(5), 1097-1117.
MLA
Panjeh Ali Beik, F. "Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations", Bulletin of the Iranian Mathematical Society, 40, 5, 2014, 1097-1117.
HARVARD
Panjeh Ali Beik F. (2014). 'Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations', Bulletin of the Iranian Mathematical Society, 40(5), pp. 1097-1117.
CHICAGO
F. Panjeh Ali Beik, "Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations," Bulletin of the Iranian Mathematical Society, 40 5 (2014): 1097-1117,
VANCOUVER
Panjeh Ali Beik F. Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations. BIMS. 2014;40(5):1097-1117.
