On the convergence of a new splitting iterative method for non-Hermitian positive definite linear systems

In this paper we present a new splitting method for solving a linear systems with non-Hermitian positive definite coefficient matrix. This splitting overcomes the computation complexity of HSS. The spectral radius and some norm properties of the iteration matrix are discussed. With the results obtained, we study the reasonable choices of the parameter and introduce a preconditioner. Moreover, an accelerated algorithm is proposed. Finally, the numerical examples show the new method is much more efficient than the HSS (or the NSS and the PSS) iteration method.