AOR收敛的一个充分必要条件

A NECESSARY AND SUFFICIENT CONDITION FOR THE CONVERGENCE OF AN AOR ITERATIVE METHOD

1.引 言 自1978年Hadjidimos提出解线性代数方程组的快速超松弛(AOR)迭代法以来,国内外许多学者对它进行了研究.在1989年的全国数值代数会议上也有一些文章专门讨论AOR方法的收敛性问题.然而以往的一些文献中往往只得出AOR收敛的一些充分条件.作者在中得出了AOR收敛、SAOR(即对称AOR)

In this paper, a necessary and sufficient condition for the convergence of an AOR iterativemethod is given under the condition that the coefficient matrix A is consistently ordered andthe eigenvalues of the Jacobi matrix of A are all real. With the same method the condition forthe convergence of the extrapolation Gauss-Seidel(EGS) method is also obtained. As an exam-ple, the conditions for the model problem are given. The rate of convergence of the EGS me-thod is about twice that of the GS method.