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. (C) 2008 Elsevier Inc. All rights reserved.