混合型方程组的数值解法

The numerical solutions of hybird systems of non-linear equations

针对混合型方程组提出一种新的迭代算法.新算法有如下特点:第一,收敛速度快,同Newton迭代法一样,新算法具有二阶收敛速度;第二,计算成本低,新算法低于Newton迭代法.在对新算法的收敛性进行严格证明的同时,数值实验还证实,新算法对初始解与精确解的接近程度的要求也比Newton迭代法有所降低.

In this paper,a new iteration method is proposed for obtaining the numerical solutions of hybrid system.including both linear and non-linear equations.The new algorithm has merits as follows.First,it converges rapidly.It is quadratic convergence the same as Newton method.Second,it is cheaper than Newton method in each iteration.The convergence is proved strictly.Relevant numerical examples are used to demonstrate the advantages of the proposed algorithm.In addition,it is demonstrated that the proposed algorithm requires the distance between the initial solution and the exact solution smaller than that of Newton method.