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

作　　者：王晓锋[1] 

机构地区：[1]渤海大学数理学院,锦州121013

出　　处：《长春理工大学学报（自然科学版）》2012年第3期114-116,119,共4页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金(11101051)

摘　　要：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.

关 键 词：非线性方程 最优阶 4阶收敛 迭代法 求根 

分 类 号：O241.7[理学—计算数学]