关于对牛顿迭代法的优化

On the Optimization of Newton’s Iterative Method

摘要: 牛顿迭代法是数值计算中最重要的常用方法之一，但是其明显缺点是每次迭代都需要函数的导数。本文利用中心差商结合弦截法对牛顿迭代法进行了改进，提出了几种改良的迭代格式。在相同函数的及初始值的前提下，数值实验显示，改进后的牛顿迭代法的迭代速度与牛顿法相比有了明显提升。

Abstract: Newton’s iterative method is one of the most important common methods in numerical calculation, but its obvious disadvantage is that each iteration needs the derivative of the function. In this paper, Newton’s iterative method is improved by using central difference quotient and chord section method, and several improved iterative schemes are proposed. Under the premise of the same function and initial value, numerical experiments show that the iteration speed of the improved Newton’s iteration method is significantly improved compared with Newton’s method.