一种基于Chebyshev迭代解非线性方程组的方法

doi:10.12286/jssx.2015.1.14

计算数学 ›› 2015, Vol. 37 ›› Issue (1): 14-20.DOI: 10.12286/jssx.2015.1.14

一种基于Chebyshev迭代解非线性方程组的方法

刘晴, 檀结庆, 张旭

合肥工业大学数学学院, 合肥 230009

收稿日期:2013-12-28 出版日期:2015-02-15 发布日期:2015-03-10
通讯作者: 张旭, Email: zhangxu8587@126.com.
基金资助:
国家自然科学基金-广东联合基金重点项目(U1135003)和国家自然科学基金项目(61070227).

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刘晴, 檀结庆, 张旭. 一种基于Chebyshev迭代解非线性方程组的方法[J]. 计算数学, 2015, 37(1): 14-20.

Liu Qing, Tan Jieqing, Zhang Xu. A METHOD BASED ON CHEBYSHEV ITERATION FOR SOLVING THE SYSTEM OF NONLINEAR EQUATIONS[J]. Mathematica Numerica Sinica, 2015, 37(1): 14-20.

A METHOD BASED ON CHEBYSHEV ITERATION FOR SOLVING THE SYSTEM OF NONLINEAR EQUATIONS

Liu Qing, Tan Jieqing, Zhang Xu

School of Mathematics, Hefei University of Technology, Hefei 230009, China

Received:2013-12-28 Online:2015-02-15 Published:2015-03-10

本文根据牛顿迭代和Chebyshev迭代法给出了一种新的迭代方法,该方法有较高的收敛阶,并在理论上给予了证明.最后给出了四个实例,将本文的实验结果与现有的几种方法的实验结果进行比较,表明我们的方法迭代次数少,有明显的优势.

关键词： 非线性方程组, Newton迭代法, Chebyshev迭代法, 收敛阶

In this paper, we derive a new iterative method, which is based on Newton and Chebyshev iteration, to solve the system of nonlinear equations with order of convergence higher than other competitive methods. Numerical examples are given to show that the proposed method outperforms the existing methods in that it has less iterations.

Key words: System of nonlinear equations, Chebyshev iterative method, Newton's method, Convergence order

MR(2010)主题分类:

65H10

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摘要

一种基于Chebyshev迭代解非线性方程组的方法

A METHOD BASED ON CHEBYSHEV ITERATION FOR SOLVING THE SYSTEM OF NONLINEAR EQUATIONS

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