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The Numerical Factorization of Polynomials

文献类型：期刊论文

作者Wu, Wenyuan1; Zeng, Zhonggang2
刊名FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
出版日期2017-02-01
卷号17期号:1页码:259-286
关键词Numerical polynomial factorization Ill-posed problem Factorization manifold Sensitivity
ISSN号1615-3375
DOI10.1007/s10208-015-9289-1
通讯作者Zeng, ZG (reprint author), NE Illinois Univ, Dept Math, Chicago, IL 60625 USA.
英文摘要Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper formulates the notion of numerical factorization based on the geometry of polynomial spaces and the stratification of factorization manifolds. Furthermore, this paper establishes the existence, uniqueness, Lipschitz continuity, condition number, and convergence of the numerical factorization to the underlying exact factorization, leading to a robust and efficient algorithm with a MATLAB implementation capable of accurate polynomial factorizations using floating point arithmetic even if the coefficients are perturbed.
资助项目NSF[DMS-0715127] ; [NSFC 11471307] ; [11171053]
WOS研究方向Computer Science ; Mathematics
语种英语
WOS记录号WOS:000393669300008
出版者SPRINGER
源URL[http://172.16.51.4:88/handle/2HOD01W0/258]  
专题自动推理与认知研究中心
通讯作者Zeng, Zhonggang
作者单位1.Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Chongqing Key Lab Automated Reasoning & Cognit, Chongqing, Peoples R China
2.NE Illinois Univ, Dept Math, Chicago, IL 60625 USA
推荐引用方式
GB/T 7714		 Wu, Wenyuan,Zeng, Zhonggang. The Numerical Factorization of Polynomials[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS,2017,17(1):259-286.
APA Wu, Wenyuan,&Zeng, Zhonggang.(2017).The Numerical Factorization of Polynomials.FOUNDATIONS OF COMPUTATIONAL MATHEMATICS,17(1),259-286.
MLA Wu, Wenyuan,et al."The Numerical Factorization of Polynomials".FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 17.1(2017):259-286.

入库方式： OAI收割

来源：重庆绿色智能技术研究院

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