TY - JOUR
ID - 555
TI - Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Panjeh Ali Beik, F.
AD - Vali-Asr University of Rafsanjan
Y1 - 2014
PY - 2014
VL - 40
IS - 5
SP - 1097
EP - 1117
KW - Linear matrix equation
KW - Krylov subspace
KW - global GMRES
KW - Schur complement
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_555.html
L1 - http://bims.iranjournals.ir/article_555_436d6ad5ed75e3a57eae6a19e45899b6.pdf
ER -