Amendment Is Not About The Z-matrix Gauss - Seidel Iterative Method Of Spectral Radius Monotonicity

In this paper, we consider the optimal parameter vector a of the modified incomplete Gauss_Seidel method(MIGS).We prove that the spectral radius functionρα of the iterative matrix Tα of MIGS with parameter vector α is strictlymonotonic decreasing with respect to a satisfying 0 ≤ α ≤ e if the classical Gauss_Seidel method converges for a Z_matrix.Some properties of the left and right eigenvectors corresponding to the largest eigenvalue in modulus are given,too.These results are useful to find an optimal parameter for MIGS. Some illustrative examples are given.