Computing real witness points of positive dimensional polynomial systems

doi:10.1016/j.tcs.2017.03.035

CORC > 重庆绿色智能技术研究院 > 中国科学院重庆绿色智能技术研究院 > 自动推理与认知研究中心

	Computing real witness points of positive dimensional polynomial systems
	Wu, Wenyuan1 ; Reid, Greg 2; 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.