A new splitting and preconditioner for iteratively solving non-Hermitian positive definite systems

A new iteration method for solving a linear system with coefficient matrix being non-Hermitian positive definite is presented in this note. We study the spectral radius and contraction properties of the iteration matrix and then analyze the best possible choice of the parameter. With the results obtained, we show that the new method is convergent for a non-Hermitian positive definite linear system and propose a preconditioner to improve the condition number of the system. The numerical examples show that the new method is much more efficient than the HSS (or PSS) iteration method.