一类非线性方程近似解的改进Newton法  

Modification of Newton's Method for Solving Nonlinear Equations

作　　者：游煦[1] 

机构地区：[1]北京石油化工学院数理系,北京102617

出　　处：《北京石油化工学院学报》2013年第3期62-66,共5页Journal of Beijing Institute of Petrochemical Technology

基　　金：北京石油化工学院青年基金资助项目;项目号:N2011-16

摘　　要：对具有任意阶导数的函数在一组线性无关的函数组下进行Taylor展开,取展开式的前2项作近似,给出在不同基函数时的改进牛顿法迭代公式,并对误差进行了分析。最后利用Matlab对一些非线性方程的近似解进行计算,并与其他算法的结果相比较。结果表明,该方法有明显优势,特别是在初始值远离近似解时收敛速度更快。First, we get the Taylor expansion of a function with arbitrary order derivative in a linearly independent functions set, take the first two expansions for approximation, and give iteration formula of modification Newton＇s method with different basis functions, such as power function and exponential function. At last, calculate the approximate solution of nonlinear equations with modification Newton＇s method by Matlab, and compare the results with other al- gorithms. This modification Newton＇s method has obvious advantages. It has faster convergence than other algorithms, especially in the initial value far away from the approximate solution.

关 键 词：非线性方程 近似解 改进Newton法 TAYLOR展开 CAUCHY定理 

分 类 号：O221[理学—运筹学与控制论]