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

文献类型：期刊论文

作者Li, Nan1; Zhi, Lihong2,3
刊名NUMERICAL ALGORITHMS
出版日期2022-02-02
页码32
关键词Polynomial system Simple multiple zero Newton's method Quadratic convergence
ISSN号1017-1398
DOI10.1007/s11075-022-01253-7
英文摘要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).
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
语种英语
WOS记录号WOS:000749427900001
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/59950]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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