求解非线性方程的一类8阶史蒂芬森型方法（英文）  

A new family of eighth-order Steffensen type methods for solving nonlinear equations

作　　者：王晓锋[1,2] 张铁[2] 

机构地区：[1]渤海大学数学系,锦州121013 [2]东北大学理学院,沈阳110819

出　　处：《黑龙江大学自然科学学报》2013年第5期611-616,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11071033)

摘　　要：针对非线性方程求根问题,提出一种三步8阶收敛的史蒂芬森型方法。在迭代过程中,本方法不需要计算任何导数,仅仅需要计算4个函数值,就可达到8阶收敛。本方法的计算效率为1.682,依据Kung与Traub提出的假设可知,新方法是最优的。数值试验证明了方法的收敛性。A family of three-step eighth-order Steffensen type methods for solving nonlinear equa- tions is presented. The new methods are free from any derivatives. Per iteration the new methods require four evaluations of the function, which implies that the efficiency index of the developed methods is 1. 682, which is optimal according to Kung and Traub＇ s conjecture. Numerical comparisons are made to show the performance of the presented methods, as shown in the illustration examoles.

关 键 词：史蒂芬森法 牛顿法 无导数 8阶收敛 

分 类 号：O241.7[理学—计算数学]