Abstract: In this paper, the author presents the convergent theorems of the improving modified Gauss-Seidel method, referred to as the IMGS method, for H-matrices as well as compare the range of parameters a_iwith the parameter ω of the SOR iterative method. The methods and results appeared in this paper are superior to those in recent results. The corresponding results in this paper also show that the IMGS method is effective to H-matrices.

Key words: Preconditioned, H-matrix, Gauss-Seidel method, M-matrix, Convergence.