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Durand-Kerner算法的全局化*

王德人 赵风光

王德人, 赵风光. Durand-Kerner算法的全局化*[J]. 应用数学和力学, 1997, 18(11): 975-986.
引用本文: 王德人, 赵风光. Durand-Kerner算法的全局化*[J]. 应用数学和力学, 1997, 18(11): 975-986.
Wang Deren, Zhao Fengguang. The Globalization of Durand-Kerner Algorithm[J]. Applied Mathematics and Mechanics, 1997, 18(11): 975-986.
Citation: Wang Deren, Zhao Fengguang. The Globalization of Durand-Kerner Algorithm[J]. Applied Mathematics and Mechanics, 1997, 18(11): 975-986.

Durand-Kerner算法的全局化*

基金项目: * 国家自然科学基金

The Globalization of Durand-Kerner Algorithm

  • 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.
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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

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