一个三阶牛顿变形方法

A Third-order Variant of Newton′s Method

基于反函数建立的积分方程,结合Simpson公式,给出了一个非线性方程求根的新方法,即为牛顿变形方法.证明了它至少三次收敛到单根,与牛顿法相比,提高了收敛阶和效率指数.文末给出数值试验,且与牛顿法和同类型牛顿变形法做了比较.结果表明方法具有较好的优越性,它丰富了非线性方程求根的方法.

Based on inverse functionrs integral equation and Simpson scheme, a new method for solving roots of non-linear equations is obtained, which,is a variant of Newton＇s method. The present method is proved to be at least third-order convergence near simple root and it improves convergence order and efficiency index compared with Newton＇s method. In the end, numerical tests are given and compared with Newton＇s method and Newton-like methods. The results show that the present method has some more advantages than others. It enriches the methods for solving the roots of non-linear equations.