Improving the modified Gauss-Seidel method for Z-matrices

In 1991 A. D. Gunawardena et al. reported that the convergence rate of the Gauss-Seidel method with a preconditioning matrix I + S is superior to that of the basic iterative method. In this paper, we use the preconditioning matrix I + S(α). If a coefficient matrix A is an irreducibly diagonally dominant Z-matrix, then [I + S(α)]A is also a strictly diagonally dominant Z-matrix. It is shown that the proposed method is also superior to other iterative methods.