A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems
文献类型：期刊论文
| 作者 | Dou, Xiaojie1; Cheng, Jin-San2
|
| 刊名 | MATHEMATICS
 |
| 出版日期 | 2018-09-01 |
| 卷号 | 6期号:9页码:18 |
| 关键词 | over-determined polynomial system isolated zeros minimum point sum of squares interval methods |
| ISSN号 | 2227-7390 |
| DOI | 10.3390/math6090166 |
| 英文摘要 | 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. |
| 资助项目 | NSFC[11471327] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000448141200025 |
| 出版者 | MDPI |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/31661]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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