Convergence and Comparison Theorems of the Modified Gauss-Seidel Method

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.

• Zhouji Chen

• Preconditioned linear system
• M-matrix
• Convergence
• Comparison theorem.

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