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=bAx=b, where A is a Z  -matrix. The iterative method contains an auxiliary matrix L1(D1)L1(D1) that is restricted to be nonnegative strictly lower triangular (diagonal) matrix. Comparison theorems show that the proper choice of the L1(D1)L1(D1) 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=bAx=b. Numerical results are presented.