A new deflation method for verifying the isolated singular zeros of polynomial systems

doi:10.1016/j.cam.2020.112825

	A new deflation method for verifying the isolated singular zeros of polynomial systems
	Cheng, Jin-San 2,3; Dou, Xiaojie 1; Wen, Junyi 2,3
刊名	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
	2020-10-01
卷号	376 页码:21
关键词	Polynomial system Deflation method Isolated singular zero Interval verification
ISSN号	0377-0427
DOI	10.1016/j.cam.2020.112825
英文摘要	In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input polynomials directly or the linear combinations of the related polynomials, we construct a new system, which can be used to refine or verify the isolated singular zero of the input system. In order to preserve the accuracy in numerical computation as much as possible, new variables are introduced to represent the coefficients of the linear combinations of the related polynomials. To our knowledge, it is the first time that considering the deflation problem of polynomial systems from the perspective of linear combinations. Some acceleration strategies are proposed to reduce the scale of the final system. We also give some further analysis of the tolerances we use, which can help us have a better understanding of our method. The experiments show that our method is effective and efficient. Especially, it works well for zeros with high multiplicities of large systems. It also works for isolated singular zeros of non-polynomial systems. (C) 2020 Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China (NSFC)[11471327]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000526110600008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51103]
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, Jin-San; Dou, Xiaojie
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 3.Univ Chinese Acad Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Jin-San,Dou, Xiaojie,Wen, Junyi. A new deflation method for verifying the isolated singular zeros of polynomial systems[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2020,376:21.
APA	Cheng, Jin-San,Dou, Xiaojie,&Wen, Junyi.(2020).A new deflation method for verifying the isolated singular zeros of polynomial systems.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,376,21.
MLA	Cheng, Jin-San,et al."A new deflation method for verifying the isolated singular zeros of polynomial systems".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 376(2020):21.