A note on the numerical approximate solutions for generalized Sylvester matrix equations with applications

In the present paper, we propose a Krylov subspace method for solving large and sparse generalized Sylvester matrix equations. The proposed method is an iterative projection method onto matrix Krylov subspaces. As a particular case, we show how to adapt the ILU and the SSOR preconditioners for solving large Sylvester matrix equations. Numerical examples and applications to some PDE’s will be given.