解非线性方程组的两种区间松弛法

Two Interval Relaxation Methods for Solving System of Nonlinear Equations

基于矩阵分裂与区间松弛算子导出了两种区间松弛迭代法，方法不用求矩阵 的逆且比已知的Ｈａｎｓｅｎ迭代法更快地收敛到解；其中有些算法具有平方收敛。此外， 应用Ｎｅｗｔｏｎ—ＳＯＲ方法构造的点序列比区间的边界序列更快地收敛到解。文中还给出 数值例子。

On the basis of the splitting matirx and the introduction of interval relaxation operators, two new interval relaxation iteration methods are presented. The new algorithm need not compute inverse matrix and they converge faster to the solution than the known Hansen interval method. In some cases square convergence occurs. In addition, apply the Newton SOR method for constructing a sequence of real vectors which converges faster to the solution. Some numerical examples are given.