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A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems
Dou, Xiaojie1; Cheng, Jin-San2
2018-09-01
Source PublicationMATHEMATICS
ISSN2227-7390
Volume6Issue:9Pages:18
AbstractIn 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.
Keywordover-determined polynomial system isolated zeros minimum point sum of squares interval methods
DOI10.3390/math6090166
Language英语
Funding ProjectNSFC[11471327]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000448141200025
PublisherMDPI
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31662
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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