ON SOME NEW CRITERIA OF CONVERGENCE OF THE GAUSS-SEIDEL ITERATION
关于Gauss-Seidel迭代收敛的新判据

In this paper, we consider some new criteria of convergence of the Gauss-Seidel iteration, the estimation of its speed of convergence, and the method to cheek the condition of these criteria. Four theorems are proved. These new criteria allow three norms of the coefficient matrix A of the equation X=AX+b to be greater than 1. They are applicable to wider situations than ather criteria now in common use and are easy to be check. In addition, the estimation of the speed of convergence is more accurate.