A single-step iteration method for non-Hermitian positive definite linear systems

An efficient single-step iteration method is presented for solving the large sparse non-Hermitian positive definite linear systems. We theoretically prove that this method converges to the unique solution of the system of linear equations under suitable restrictions. Moreover, we derive an upper bound for the spectral radius of the new iteration matrix. Furthermore, we consider acceleration of the new iteration by Krylov subspace methods and some special properties of the new preconditioned matrix are proposed. Numerical experiments on a few model problems are presented to further examine the effectiveness of our new method.