The Numerical Factorization of Polynomials
文献类型:期刊论文
作者 | Wu, Wenyuan1![]() |
刊名 | FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
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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 |
DOI | 10.1007/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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