一种牛顿迭代法的改进——牛顿弦割迭代法

An Improvement of Newton’s Method —Newton’s Chord Secant Method

牛顿迭代法是非线性方程求根的一个常用的方法,它具有至少二阶的收敛速度,但是需要计算一阶导数值。本文针对牛顿迭代法进行改进,以弦割代替导数,只需计算函数值,不需计算一阶导数值,同样也具有至少二阶的收敛速度,并且形式简单,计算量小,数值试验表明该迭代公式十分有效。

Newton’s method is a commonly used way to find roots of nonlinear equations. It has at least the second-order convergence rate, but it needs to calculate the first-order derivative value. In this paper, the Newton method is improved. The derivative is replaced by a chord secant. It only needs to calculate the value of the function and does not need to calculate the value of the first derivative. It also has at least the second order of convergence speed, and the form is simple and the calculation amount is small. Numerical experiments show that the iterative formula is very effective.