4阶收敛的史蒂芬森型迭代格式(英文)  

A Steffensen Type Method with Fourth-order Convergence

作　　者：王晓锋[1,2] 张铁[2] 

机构地区：[1]渤海大学数理学院,辽宁锦州121013 [2]东北大学理学院,辽宁沈阳110819

出　　处：《哈尔滨理工大学学报》2013年第3期91-94,101,共5页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11071033;11101051)

摘　　要：针对非线性方程求根问题,提出了一种4阶收敛的史蒂芬森型方法.在迭代过程中新方法不需要计算任何导数,仅仅需要计算3个函数值,就可达到4阶收敛.该方法的计算效率为1.587.依据Kung与Traub提出的假设,即若一个迭代法在迭代过程中需要计算n个函数值,则该方法能达到最优收敛阶为2n-1.可知当n=3时,新方法是最优的.数值试验进一步证明了该方法的收敛性.In this paper, a Steffensen type method of fourth-order convergence for solving nonlinear equations is suggested. The derivative-free method only uses three evaluations of the function per iteration to achieve fourth- order convergence. Therefore, the new method has an efficiency index equal to 1. 587. Kung and Traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2^n- 1 The new method agrees with Kung-Traub conjecture for n = 3. Numerical comparisons are made to show the performance of the presented method, as shown in the illustration examples.

关 键 词：史蒂芬森法 牛顿法 无导数 4阶收敛 求根 

分 类 号：O241.7[理学—计算数学]