摘要
弦割法、Muller法与牛顿法一样,都是求解非线性方程的著名算法之一.然而在目前众多优秀的数值分析教材或论著中,关于弦割法和Muller法收敛阶的证明过程都是比较复杂的,无一例外的都是借助于差分方程的求解.本文对这两个算法的收敛阶给出了一种新的简单、直接的证明方法,达到了与牛顿法收敛阶证明方法的统一,同时还能够方便地求出它们的渐近误差常数.
The secant method,Muller＇s method and Newton＇s method are all famous methods for solving nonlinear equations.However,in currently numerous excellent numerical analysis textbooks,the proof process about the convergence order of the secant Method and Muller＇s Method is all complicated,all given by the solving of difference equation.This paper gives a new simple and direct proof method to the convergence orders of these two methods as same as the proof method of the convergence order of Newton＇s method,and obtains their asymptotic error constant synchronously.
出处
《大学数学》
2011年第2期107-110,共4页
College Mathematics
基金
河南省高等教育改革研究项目
关键词
非线性方程
牛顿法
弦割法
Muller法
渐近误差常数
nonlinear equation
Newton＇s method
the secant method
Muller＇s method
asymptotic error constant
