Right Preconditioned MINRES Using Eisenstat SSOR for Positive Semidefinite Systems

Abstract

Abstract. Consider solving large sparse symmetric positive semidefinite linear systems. Since CG may not converge for inconsistent systems, we use MINRES. We will use right preconditioning for MINRES, since it is easier to preserve the equivalence of the problem, especially for the inconsistent case. We first introduce the algorithm for the right preconditioned MINRES. Then, we propose the right preconditioned MINRES using Eisenstat SSOR. Some numerical experiments indicate that the right preconditoned MINRES using Eisenstat SSOR is efficient and robust. Finally, we show that the residual norm can be further reduced by restarting the method.