AOR interative methods under the preconditioned matrix I+S+R

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.