弦截法的超线性收敛性验证  

Validation of Superlinear Covergence of Secant Method

作　　者：邢进良[1] 

机构地区：[1]沙洋师范高等专科学校数理系,湖北荆门448200

出　　处：《孝感学院学报》2007年第3期56-59,共4页JOURNAL OF XIAOGAN UNIVERSITY

摘　　要：弦截法的基本思想是利用函数值f(xk+1),f(xk)来回避导数值f′(xk)的计算,本文利用最小二乘法验证了弦截法的迭代收敛阶数p=1.618,并增加了修正因子使验证结果更准确。同时,提出了该验证算法的实验步骤,通过一个特定方程根的求解实例,验证了其收敛阶数,并比较了牛顿法和弦截法的迭代收敛性能。The elementary idea of secant method is that one can avoid calculatingf （xk） usingf（xk＋1 ）, f （xk）. By using least square method, the author validates the convergence order of secant method to be 1. 618. Furthermore, the validation in the paper is more accurate by adding modifying factors. In addition, the author provides the validation algorithm and compares the convergence of secant method with that of Newton method by solving a specific equation.

关 键 词：弦截法 超线性收敛性 最小二乘法 修正因子 

分 类 号：O241[理学—计算数学]