关键词: 预条件子, Gauss-Seidel 迭代, AOR迭代, M -矩阵,  , 线性系统

Abstract:

In this paper, by comparing with the spectral radiuses of the iterative methods, the authors prove, for the first time, that the IMGS method^[1-2] with the preconditioner I+S_α is faster than the basic AOR iterative method, and then prove that the preconditioned SOR method is 
faster than the basic SOR method. Finally, the authors prove the monotony of the spectral radius with respect to the parameter and 
improve some recent known results.

Key words: Preconditioner, Gauss-Seidel iteration, AOR iteration, M-matrix, Linear system