Computing real witness points of positive dimensional polynomial systems | |
Wu, Wenyuan1; Reid, Greg2; Feng, Yong1 | |
刊名 | THEORETICAL COMPUTER SCIENCE |
2017-06-12 | |
卷号 | 681页码:217-231 |
关键词 | Numerical algebraic geometry Real algebraic geometry Homotopy continuation Singular critical points Real witness points |
ISSN号 | 0304-3975 |
DOI | 10.1016/j.tcs.2017.03.035 |
通讯作者 | Wu, WY (reprint author), Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Chongqing Key Lab Automated Reasoning & Cognit, Beijing, Peoples R China. |
英文摘要 | We consider a critical point method for finding certain solution (witness) points on real solution components of real polynomial systems of equations. The method finds points that are critical points of the distance from a plane to the component with the requirement that certain regularity conditions are satisfied. In this paper we analyze the numerical stability and complexity of the method. We aim to find at least one well conditioned witness point on each connected component by using perturbation, path tracking and projection techniques. An optimal-direction strategy and an adaptive step size control strategy for path following on high dimensional components are given. (C) 2017 Elsevier B.V. All rights reserved. |
资助项目 | Key Research Program of Frontier Sciences of CAS[QYZDB-SSW-SYS026] ; Key Research Program of Frontier Sciences of CAS[cstc2015jcyjys40001] ; NSFC[11471307] ; NSFC[11671377] |
WOS研究方向 | Computer Science |
语种 | 英语 |
出版者 | ELSEVIER SCIENCE BV |
WOS记录号 | WOS:000404502300014 |
内容类型 | 期刊论文 |
源URL | [http://172.16.51.4:88/handle/2HOD01W0/210] |
专题 | 自动推理与认知研究中心 中国科学院重庆绿色智能技术研究院 |
通讯作者 | Wu, Wenyuan |
作者单位 | 1.Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Chongqing Key Lab Automated Reasoning & Cognit, Beijing, Peoples R China 2.Western Univ, Appl Math Dept, London, ON, Canada |
推荐引用方式 GB/T 7714 | Wu, Wenyuan,Reid, Greg,Feng, Yong. Computing real witness points of positive dimensional polynomial systems[J]. THEORETICAL COMPUTER SCIENCE,2017,681:217-231. |
APA | Wu, Wenyuan,Reid, Greg,&Feng, Yong.(2017).Computing real witness points of positive dimensional polynomial systems.THEORETICAL COMPUTER SCIENCE,681,217-231. |
MLA | Wu, Wenyuan,et al."Computing real witness points of positive dimensional polynomial systems".THEORETICAL COMPUTER SCIENCE 681(2017):217-231. |
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