Durand-Kerner算法的全局化<sup>*</sup>

王德人; 赵风光

Durand-Kerner算法的全局化^*

王德人¹,
赵风光²

1.
上海大学数学系, 上海 201800;
2.
复旦大学, 上海 200433

基金项目: * 国家自然科学基金

计量
- 文章访问数: 2033
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- 被引次数: 0
出版历程
- 收稿日期: 1995-10-16
- 修回日期: 1997-06-23
- 刊出日期: 1997-11-15

The Globalization of Durand-Kerner Algorithm

Wang Deren¹,
Zhao Fengguang²

1.
Shanghai University. Shanghai 201800, P. R. China;
2.
Fudan University, Shanghai 200433, P. R. China

摘要

摘要: 本文利用对称多项式与一元多项式之间的关系,结合连续同伦思想,构造了一条概率为1的正则同论曲线.然后,对这条同论路径,进行离散化跟踪,导出了一类带有步长参数的Durand-Kerner算法,我们证明了这类算法的整体收敛性,从而在理论上解决了人们关于Durand-Kerner算法具有整体性的推测.本文还深入讨论了步长参数的选择问题.最后,我们以足够的数值例子,检验了理论的正确性.
- Durand-Kerner算法 /
- 连续同伦 /
- 路径跟踪 /
- 整体收敛性 /
- 点估计
Abstract: Making use of the theory of continuous ho motopy and the relation between symmetric polynomial and polynomial in one variable the authors devoted this article to constructing a regularly homotopic curve with probability one, Discrete tracing along this homotopic curve leads to a class of Durand-Kerner algorithm with step parameters.The convergence of this class of algorithms is given, whick solves the conjecture about the global property of Durand-Kerner algorithm,The problem for steplength selection is thoroughly discussed,Finally,sufficient numerical examples are used to verify our theory.
- Durand-Kerner algorithm /
- continuous homotopy /
- path tracing /
- global convergence /
- point estimation

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参考文献(19)

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