Preconditioned Global FOM and GMRES Methods for Solving Lyapunov Matrix Equations

This paper presents, a preconditioned version of global FOM and GMRES methods for solving Lyapunov matrix equations AX +XAT = −BTB. These preconditioned methods are based on the global full orthogo-nalization and generalized minimal residual methods. For constructing effective preconditioners, we will use ADI spiliting of above lyapunov matrix equations. Numerical experiments show that the solution of Lyapunov matrix equation can be obtained with high accuracy by us-ing the preconditioned version of global FOM and GMRES algorithms and this version are more robust and more efficient than those without preconditioning