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

doi:10.1016/j.cam.2020.112825

CSpace

	A new deflation method for verifying the isolated singular zeros of polynomial systems
	Cheng, Jin-San 1,3; Dou, Xiaojie 2; Wen, Junyi 1,3
	2020-10-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	376 页码:21
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.
关键词	Polynomial system Deflation method Isolated singular zero Interval verification
DOI	10.1016/j.cam.2020.112825
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China (NSFC)[11471327]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000526110600008
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51104
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.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Civil Aviat Univ China, Coll Sci, Tianjin 300300, 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.