解非线性方程的一种新的三步六阶迭代格式  

A New Three-Step Sixth Order Iterative Scheme for Solving Nonlinear Equations

作　　者：黄丝引 曾光 张思平 余笑宇 雷莉 HUANG Siyin;ZENG Guang;ZHANG Siping;YU Xiaoyu;LEI Li(School of Science,East China University of Technology,330013,Nanchang,PRC)

机构地区：[1]东华理工大学理学院,南昌330013

出　　处：《江西科学》2022年第1期17-21,共5页Jiangxi Science

基　　金：江西省教育厅科学技术研究项目(GJJ200757)。

摘　　要：Newton迭代法是求解非线性方程的重要方法之一,其收敛阶是二阶,在迭代过程中需要计算一个函数值和一个导数值,因此Newton迭代法的效率指数为1.4142。基于Newton迭代法结合两步迭代格式构造了一种新的三步迭代格式,通过理论证明其收敛阶是六阶,在迭代过程中每次均需要计算2个函数值和2个导数值,则该三步迭代格式的效率指数为1.5651,最后数值实验结果也验证了该方法的有效性和可行性。Newton iterative method is one of the important methods to solve nonlinear equations.Its convergence order is second order.In the iterative process,a function value and a derivative value need to be calculated.Therefore,the efficiency index of Newton iterative method is 1.4142.In this paper,a new three-step iterative scheme is constructed based on Newton iterative method combined with a two-step iterative scheme.It is proved that its convergence order is order 6.In the iterative process,two function values and two derivatives need to be calculated each time.Therefore,the efficiency index of the three-step iterative scheme is 1.5651.Finally,the numerical experimental results also verify the effectiveness and feasibility of the method.

关 键 词：NEWTON迭代法 收敛阶 非线性方程 

分 类 号：O175[理学—数学]