A generalized two-sweep shift splitting method for non-Hermitian positive definite linear systems

In this paper, based on the shift splitting of the coefficient matrix, a generalized two-sweep shift splitting (GTSS) method is introduced to solve the non-Hermitian positive definite linear systems. Theoretical analysis shows that the GTSS method is convergent to the unique solution of the linear systems under a loose restriction on the iteration parameter. Numerical experiments are reported to the efficiency of the GTSS method.