A numerical method for computing border curves of bi-parametric real polynomial systems and applications

doi:10.1007/978-3-319-45641-6_11

CORC > 重庆绿色智能技术研究院 > 中国科学院重庆绿色智能技术研究院 > 自动推理与认知研究中心

	A numerical method for computing border curves of bi-parametric real polynomial systems and applications
	Chen, Changbo; Wu, Wenyuan
	2016
会议日期	September 19, 2016 - September 23, 2016
会议地点	Bucharest, Romania
DOI	10.1007/978-3-319-45641-6_11
页码	156-171
通讯作者	Wu, Wenyuan (wuwenyuan@cigit.ac.cn)
英文摘要	For a bi-parametric real polynomial system with parameter values restricted to a finite rectangular region, under certain assumptions, we introduce the notion of border curve. We propose a numerical method to compute the border curve, and provide a numerical error estimation. The border curve enables us to construct a so-called “solution map”. For a given value u of the parameters inside the rectangle but not on the border, the solution map tells the subset that u belongs to together with a connected path from the corresponding sample point w to u. Consequently, all the real solutions of the system at u (which are isolated) can be obtained by tracking a real homotopy starting from all the real roots at w throughout the path. The effectiveness of the proposed method is illustrated by some examples. © Springer International Publishing AG 2016.
会议录	18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016
语种	英语
电子版国际标准刊号	16113349
ISSN号	03029743
内容类型	会议论文
源URL	[http://119.78.100.138/handle/2HOD01W0/4833]
专题	自动推理与认知研究中心
作者单位	Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Beijing, China
推荐引用方式 GB/T 7714	Chen, Changbo,Wu, Wenyuan. A numerical method for computing border curves of bi-parametric real polynomial systems and applications[C]. 见:. Bucharest, Romania. September 19, 2016 - September 23, 2016.