一类解非线性方程的不需要计算导数的新方法

A new method for solving nonlinear equation without derivative calculation

为解决Newton迭代法求非线性方程数值解时必须提供一阶导数值的问题,提出了一个新的迭代方法,该方法不需提供导数值而只需计算函数值,且具有p=1.839的收敛阶,因而是一个收敛速度快且不需要计算导数值的迭代方法.最后给出了数值试验,计算结果表明,该方法是非常有效的.

Aimed at the calculation complexity of Newton iterative method for solving nonlinear equation, a new iterative method with higher convergence rate and without derivative calculation is presented in this paper. Its convergence rate p is 1. 839 and it doesn＇ t need to calculate derivative. The numerical experient is given, and the calculation result shows that this method is effective.