Note to the mixed-type splitting iterative method for Z-matrices linear systems

In this paper, the mixed-type splitting iterative method is established for solving the linear system Ax = b , where A is a Z-matrix. The iterative method contains an auxiliary matrix L 1 ( D 1 ) that is restricted to be nonnegative strictly lower triangular (diagonal) matrix. Comparison theorems show that the proper choice of the L 1 ( D 1 ) can lead to the convergence rate of the Mixed-Type Iterative Method faster than that of the SOR and AOR type iterative methods for solving Ax = b . Numerical results are presented.