Improved two-step Newton's method for computing simple multiple zeros of polynomial systems

doi:10.1007/s11075-022-01253-7

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	Improved two-step Newton's method for computing simple multiple zeros of polynomial systems
	Li, Nan 1; Zhi, Lihong 2,3
	2022-02-02
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
页码	32
摘要	Given a polynomial system f that is associated with an isolated singular zero xi whose Jacobian matrix is of corank one, and an approximate zero x that is close to xi, we propose an improved two-step Newton's method for refining x to converge to xi with quadratic convergence. Our new approach is based on a closed-form basis of the local dual space and a recursive reduction of the simple multiple zero. By avoiding solving several least-squares problems which appeared in the previous methods, an overall 2 x-5 x acceleration is achieved. The proof of the quadratic convergence of proposed iterations is also simplified significantly. Numerical experiments demonstrate up to 100 x speed-up when we replace the least-squares-solving calculations with closed-form solutions for refining approximate singular solutions of large-size problems (1000 equations and 1000 variables).
关键词	Polynomial system Simple multiple zero Newton's method Quadratic convergence
DOI	10.1007/s11075-022-01253-7
收录类别	SCI
语种	英语
资助项目	National Key Research Project of China[2018YFA0306702] ; National Natural Science Foundation of China[12071467] ; National Natural Science Foundation of China[12171324]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000749427900001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59951
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Nan
作者单位	1.Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Guangdong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Li, Nan,Zhi, Lihong. Improved two-step Newton's method for computing simple multiple zeros of polynomial systems[J]. NUMERICAL ALGORITHMS,2022:32.
APA	Li, Nan,&Zhi, Lihong.(2022).Improved two-step Newton's method for computing simple multiple zeros of polynomial systems.NUMERICAL ALGORITHMS,32.
MLA	Li, Nan,et al."Improved two-step Newton's method for computing simple multiple zeros of polynomial systems".NUMERICAL ALGORITHMS (2022):32.