摘要非线性方程大量地出现在描述现实社会各种现象的数学模型中,它们常比线性方程更贴合实际.求得非线性问题的精确解是很困难的,所以我们常用迭代法求解非线性方程的问题,常用的迭代法有对分法、不动点迭代法、牛顿法、割线法等.这些迭代方法的基本思想是通过不同的方法寻找方程的等价形式,从代数角度或是几何角度求得等价形式的不动点的近似值,从而得到方程的近似解.

由单变量非线性方程的求解方法问题可以推广到多变量非线性方程组问题的求解,常用的迭代方法有不动点迭代法、牛顿法等.61871

本文主要介绍非线性方程与非线性方程组的常用迭代法,并给出其相应的Matlab程序以及数值例子.

毕业论文关键词 : 非线性方程;非线性方程组; 迭代法; Matlab程序

Nonlinear equation’s iteration methods and its Matlab programs

Abstract Mathematic models that describe social phenomenon need nonlinear equation which is more suitable of practical than linear equation. It is difficult to find nonlinear equation’s accurate solution, so iterations are widely used in solving nonlinear equation. Several iterations, which are adopted frequently, are Bisection method, Fixed-point iteration method, Newton method, Secant Approach method and so on. The basic idea of these methods is to find equivalent form of nonlinear equation in various ways, and solving nonlinear equation’s approximate solution by solving the equivalent form’s approximate solution of the fixed point through algebra or geometry way. 

Generally speaking, solving nonlinear equations always involve nonlinear equation problem with single variable generalizing to nonlinear equations problem with several variables. The iterations, which are commonly used, are Fixed-point iteration methods, Newton method, and so on.

In this paper, we have discussed some iteration methods for single nonlinear equation and nonlinear equations. And then, we have introduced some iteration methods with Matlab programs and numerical examples. 

Keywords: nonlinear equation; nonlinear equations; iteration methods; Matlab program 

目  录

摘  要 I

Abstract II

前 言 2

第一章 常用非线性方程求解的迭代方法 4

1. 对分法 4

2. 不动点迭代法 8

3. 牛顿法 13

4. 割线法 18

第二章 几种求解非线性方程迭代法的比较 22

1. 不动点迭代法 22

2. 牛顿法 23

3. 割线法 23

第三章 两个变量的非线性方程组求解的迭代法 25

1. 不动点迭代法 25

2. 牛顿法 26

第四章 总结 29

参考文献 30

致  谢 31

前 言在科技飞速发展的今天,在很多领域都涉及了非线性方程求解问题.例如利用非线性方程对生物量进行估计、基于非线性方程的鱼眼图像畸变矫正以及大量的非线性方程（组）求解各类物理问题. 非线性方程的迭代法及其Matlab程序:http://www.youerw.com/shuxue/lunwen_43798.html