Vol.3 No.02(2014), Article ID:13569,6 pages
DOI:10.12677/AAM.2014.32014

A Numerical Method for Solving the Nonlinear Algebraic Equations

Yanan Zhou

Yangtze College, East China Institute of Technology, Fuzhou

Email: 2318284432@qq.com

Received: Mar. 22nd, 2014; revised: Apr. 18th, 2014; accepted: Apr. 26th, 2014

ABSTRACT

In this paper, we will use a new method of elimination and the dichotomy of the nonlinear equation to common research the numerical solution of equations.

Keywords:A New Method of Elimination, Dichotomy

Email: 2318284432@qq.com

1. 引言

(1)

2. 消元法

(2)

(3)

(4)

(5)

(6)

(7)

(8)

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(10)

(k为可约次数)         (11)

(12)

3. 数值解法的实现

3.1. 消元法在非线性代数方程组的数值解法上的应用

3.2. 解法的收敛速度

3.3. 解法的精度

(13)

4. 实例

4.1. 线性方程组的实例

(14)

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4.2. 非线性代数方程组的实例

(24)

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(26)

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4.3. 利用牛顿法得到的数值解

5. 总结与讨论

Figure 1. Using the images to evaluate generally small range of

Table 1. The elimination method and Newton iteration accuracy comparison in this paper

1. [1]   张平文, 李铁军 (2007) 数值分析. 北京大学出版社, 北京, 110-131.

2. [2]   Zhou, Y.N. (2014) A kind of proof about triangles’s congruent and a new kind of elimination method. Open Science Repository Mathematics, e23050492.

3. [3]   吴文俊 (2000) 数学机械化. 科学出版社, 北京.