求解带不可微项方程的一种改进的弦截法  

An Improved Secant Method for Solving the Equations with Non-Differential Term

作　　者：王树忠[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2011年第4期118-120,125,共4页Journal of Harbin University of Science and Technology

基　　金：黑龙江省自然基金资助项目(A200811);黑龙江省教育厅科学技术研究项目(11521045)

摘　　要：针对带不可微项方程的求解问题,给出了一种改进的弦截法.该方法在迭代过程中不需要计算函数的导数值,而是用函数的均差来替代导数值.利用优序列技巧,在γ-条件下,证明了该迭代格式的收敛性,并给出了误差估计.得到的结果为:当判据α满足一定条件时,该迭代格式所产生的向量序列{zn}与{wn}均收敛于带不可微项方程的唯一解z*.In this paper,an improved secant method is given to solve the equations with non-differential terms.In the iterative process,this method uses the different quotient to replace the derivative value without calculating it.Under the γ-condition,the convergence theorem is proven and the error estimation is obtained by the technique of major function sequences.The result is as follows： If α satisfies some condition,then the sequences{zn},{wn}produced by the iteration scheme given in the paper,converge to the solution of the equations with non-differential term.

关 键 词：不可微项 Γ-条件 优函数 收敛性 弦截法 

分 类 号：O241.7[理学—计算数学]