Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations
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Abstract:
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.
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Journal title
volume 40 issue 5
pages 1097- 1117
publication date 2014-10-01
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