CSpace  > 系统科学研究所
 A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems Dou, Xiaojie1; Cheng, Jin-San2 2018-09-01 Source Publication MATHEMATICS ISSN 2227-7390 Volume 6Issue:9Pages:18 Abstract 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. Keyword over-determined polynomial system isolated zeros minimum point sum of squares interval methods DOI 10.3390/math6090166 Language 英语 Funding Project NSFC[11471327] WOS Research Area Mathematics WOS Subject Mathematics WOS ID WOS:000448141200025 Publisher MDPI Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/31662 Collection 系统科学研究所 Corresponding Author Cheng, Jin-San Affiliation 1.Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China Recommended CitationGB/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.
 Files in This Item: There are no files associated with this item.
 Related Services Recommend this item Bookmark Usage statistics Export to Endnote Google Scholar Similar articles in Google Scholar [Dou, Xiaojie]'s Articles [Cheng, Jin-San]'s Articles Baidu academic Similar articles in Baidu academic [Dou, Xiaojie]'s Articles [Cheng, Jin-San]'s Articles Bing Scholar Similar articles in Bing Scholar [Dou, Xiaojie]'s Articles [Cheng, Jin-San]'s Articles Terms of Use No data! Social Bookmark/Share