一类求解非线性方程的最优的4阶收敛的迭代法

摘要

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.%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.