求解带不可微项方程的一种改进的弦截法

摘要

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 y - 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 a 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.%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y一条件下,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*.