TY - JFULL AU - Zhouji Chen PY - 2013/12/ TI - Convergence and Comparison Theorems of the Modified Gauss-Seidel Method T2 - International Journal of Mathematical and Computational Sciences SP - 1631 EP - 1635 VL - 7 SN - 1307-6892 UR - https://publications.waset.org/pdf/9997451 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 83, 2013 N2 - In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented new preconditioner. ER -