A new preconditioner for indefinite and asymmetric matrices

We present a novel preconditioner for numerical solutions of large sparse linear systems with indefinite and asymmetric matrices. This new preconditioner named as product preconditioner(PS) is constructed by two fairly simple preconditioners. The distribution of eigenvalues and the form of the eigenvectors of the preconditioned matrix are analyzed. Moreover, an upper bound on the degree of the minimal polynomial is also studied. Numerical experiments with several examples show that the proposed PS performs better than block diagonal preconditioner(BD) and block triangular preconditioner (BT) as well as the constraint preconditioner(SC) in terms of the number of iteration and computational time.