一类新的求解非线性方程的七阶方法

A New Familiy of Seventh-Order Methods for Solving Non-Linear Equations

利用权函数法给出了一类求解非线性方程单根的七阶收敛的方法.每步迭代需要计算三个函数值和一个导数值,因此方法的效率指数为1.627.数值试验给出了该方法与牛顿法及同类方法的比较,显示了该方法的优越性.最后指出Kou等人给出的七阶方法是方法的特例.

In this paper, we developed a new family of seventh-order methods for solving simple roots of non-linear equations by the weight function method. Per iteration these meth- ods require three evaluations of the function and one evaluation of the first derivative, which implies that the efficiency indices is 1.627 for the seventh-order methods. These methods are comparable with Newton＇s method and the other similar methods, as shown in the illustration examples, which shows the advantages of the proposed method. Notice that Kou et al.＇s method is a special case of the developed family of seventh-order methods.