讨论了A为大型稀疏非奇异矩阵的线性方程组Ax=b的AOR迭代求解问题.在系数矩阵A为对角元素非零的(1,1)相容次序矩阵且其相应的Jacobi矩阵的特征值的平方数均为纯虚数或零的情况下,得到了AOR方法收敛的充要条件.并给出一个数值例子对结论作以说明.
The AOR iterative method for solving linear systems of the form Ax = b is discussed, where A is a large sparse nonsingular matrix. A sufficient and necessary cndition of the AOR iterative method is given in the case that the cofficient matrix A is ( 1,1 ) consistently ordered matrix and all square of the eigenvalues of its Jaco-bi matrix are pure imaginaries or zeroes. In addition, a numerical example is given for illustrating the results.