Abstract: In the present work, we propose a new method for
solving the matrix equation AXB=F . The new method can
be considered as a generalized form of the well-known global full
orthogonalization method (Gl-FOM) for solving multiple linear
systems. Hence, the method will be called extended Gl-FOM (EGl-
FOM). For implementing EGl-FOM, generalized forms of block
Krylov subspace and global Arnoldi process are presented. Finally,
some numerical experiments are given to illustrate the efficiency of
our new method.
Abstract: In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.