牛顿法的一点注记和改进

A Note and an Addition to Newton's Method

本文讨论求解非线性方程的牛顿法 ,证明牛顿法在一个弱条件下仍保持局部二阶收敛性 ,给出牛顿法的一点改进 ,即一个不带导数的单参数的二阶收敛的迭代法 ,而且分别得到这两种迭代法的收敛因子 ,最后进行数值实验 .

In this paper, Newton iteration method for solving nonlinear equations is discussed. It is proved that Newton iteration method is still quadratically convergent under a weak condition, and a new point is added to Newton's method, i.e., a quadratic convergence parametric iteration formula without derivative. Finally, some numerical experiments are performed.