A MODIFIED SSOR PRECONDITIONING METHOD FOR AUGMENTED SYSTEMS

In this paper, a modified SSOR (MSSOR) preconditioning method is proposedfor solving augmented systems. The key idea is to change the values of diagonal elements ofthe coefficient matrices in order to obtain better preconditioners for the original systems. Westudy the spectral property of the preconditioned matrix and the convergence of the MSSOR preconditioning method. Finally, numerical experiments are presented to illustrate the efficiencyof the MSSOR preconditioning method. We will see that the iterative numbers of our method toreceive the solution are better than those of some generalized iterative methods by consideringthe GMRES methods combined with the proposed MSSOR preconditioners to accelerate the convergence. In addition, we find the optimal omega is relatively steady to our methods.