新的预条件AOR迭代法的收敛性

CONVERGENCE OF THE NEW PRECONDITIONED AOR ITERATIVE METHOD

讨论Z-矩阵线性系统的一类新的预条件AOR迭代法的收敛性。对预条件后的AOR迭代法的系数矩阵进行两种不同的分裂,得到了这两种分裂下的相对应的预条件AOR迭代法的收敛速度分别与基本的AOR迭代法的收敛速度之间的比较定理。最后对这两种分裂间的预条件迭代法的收敛速度进行比较,得出比较结果。

In this paper,we discuss the convergence of a new preconditioned AOR iterative method for Z-matrices linear systems.We consider two different AOR-type splittings for the coefficient matrix of the preconditioned AOR iterative method.Furthermore,we obtain comparison theorems of the convergence rates between the corresponding AOR iterative method of the two splittings and the basic AOR iterative method respectively.Finally,we get the comparison results of the convergence rates between the corresponding AOR iterative methods of the two splittings.