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中文摘要：
对于线性方程组Ax=b,讨论了在预条件预矩阵I＋S＋R下系数矩阵为非奇异Z-阵时AOR迭代法的收敛性以及系数矩阵为非奇异不可约Z-阵时AOR方法的敛散性,进而得到了2个比较定理,并得出了预条件矩阵可以加快AOR方法的敛散速度,最后借助Matlab实现并验证了结论.
英文摘要：
On linear equations Ax=b,it is analysed the convergence of AOR iterative method under this pre-conditioned matrix I＋S＋R when coefficient matrix is nonsingular Z-matrix.At the same time,it is discussed the convergence and divergence of AOR iterative method when coefficient matrix is non-singular irreducible Z-matrix.Then two comparision theorems are obtained.The preconditioned matrix can accelerate the rate of convergence and divergence of AOR iterative method.Finally the conclusion is achieved and verified by using Matlab.
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