A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems

doi:10.3390/math6090166

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	A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems
	Dou, Xiaojie 1; Cheng, Jin-San2
	2018-09-01
发表期刊	MATHEMATICS
ISSN	2227-7390
卷号	6 期号:9 页码:18
摘要	In this paper, by transforming the given over-determined system into a square system, we prove a necessary and sufficient condition to certify the simple real zeros of the over-determined system by certifying the simple real zeros of the square system. After certifying a simple real zero of the related square system with the interval methods, we assert that the certified zero is a local minimum of sum of squares of the input polynomials. If the value of sum of squares of the input polynomials at the certified zero is equal to zero, it is a zero of the input system. As an application, we also consider the heuristic verification of isolated zeros of polynomial systems and their multiplicity structures.
关键词	over-determined polynomial system isolated zeros minimum point sum of squares interval methods
DOI	10.3390/math6090166
语种	英语
资助项目	NSFC[11471327]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000448141200025
出版者	MDPI
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31662
专题	系统科学研究所
通讯作者	Cheng, Jin-San
作者单位	1.Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Dou, Xiaojie,Cheng, Jin-San. A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems[J]. MATHEMATICS,2018,6(9):18.
APA	Dou, Xiaojie,&Cheng, Jin-San.(2018).A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems.MATHEMATICS,6(9),18.
MLA	Dou, Xiaojie,et al."A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems".MATHEMATICS 6.9(2018):18.