Durand-Kerner算法的全局化  

The Globalization of Durand-Kerner Algorithm

作　　者：王德人[1] 赵风光[2] 

机构地区：[1]上海大学数学系,上海201800 [2]复旦大学,上海200433

出　　处：《应用数学和力学》1997年第11期975-986,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金

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．Making use of the theory of continuous homotopy 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, which solves the conjecture about the global property of Durand-Kerner algorithm.The problem for steplength selection is thoroughly discussed. Finaily,sufficient numerical examples are used to verify our theory.

关 键 词：D-K算法 连续同伦 路径跟踪 全局化 多项式 重点 

分 类 号：O241.6[理学—计算数学]