一类求解非线性方程的最优的4阶收敛的迭代法

A Family of Optimal Iterative Methods with Fourth Orders Convergence For Nonlinear Equations

本文利用权函数方法给出了一类求解非线性方程单根的最优4阶收敛的迭代法。该方法每步迭代需要计算两个函数值和一个一阶导数值,因此该方法的效率指数为1.587。最后通过数值试验与其它方法进行了比较,显示了该方法的优越性。

In this paper,we present a new family of optimal fourth-order iterative methods for solving nonlinear equations by using weight function approach.Per iteration of the new method reaches optimal orders with two functional evaluations and one evaluation of first-order derivative,which implies that the efficiency indices of the new method is 1.587.Finally,numerical comparisons are made to show the performance of the presented methods,as shown in the illustration examples.