摘要
在两种三阶的牛顿变形方法的基础上,利用线性插值和待定系数法得到了两类新的牛顿变形方法.这两类方法都只增加了一个函数值就提高了原来两种三阶方法的收敛阶数和效率指数.从理论上证明了这两类方法的收敛阶都能达到五阶,其中有一种方法可以达到六阶收敛.数值实验结果验证了此方法的有效性,丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值.
In this paper,based on two kinds of three-order variant of Newton methods,we use the linear interpolation and the method of undetermined coefficients to present two new families of iterative method for solving nonlinear equations.These two families of iterative mdhod improve the order of convergence and the efficiency index of those two kinds of third order methods.It is proved that the orders of convergence of these two families methods are five.And one of them can coverge to six order.Several numberical examples are given to demonstrate the effectiveness of the presented methods by comparing with some other methods.they enrich the methods to find the roots of nonlinear equations and have great value in both theory and application.
出处
《安徽师范大学学报（自然科学版）》
CAS
北大核心
2013年第5期430-436,共7页
Journal of Anhui Normal University(Natural Science)
基金
国家自然科学基金(61272024)
关键词
牛顿迭代
非线性方程
收敛阶
迭代方法
数值实验
newton＇s iteration
nonlinear equations
convergence order
iterative methods
numerical text
