THE PSLQ ALGORITHM FOR EMPIRICAL DATA
文献类型：期刊论文
| 作者 | Feng, Yong ; Chen, Jingwei; Wu, Wenyuan
|
| 刊名 | MATHEMATICS OF COMPUTATION
 |
| 出版日期 | 2019-05-01 |
| 卷号 | 88期号:317页码:1479-1501 |
| 关键词 | Integer relation PSLQ empirical data |
| ISSN号 | 0025-5718 |
| DOI | 10.1090/mcom/3356 |
| 通讯作者 | Feng, Yong(yongfeng@cigit.ac.cn) |
| 英文摘要 | The celebrated integer relation finding algorithm PSLQ has been successfully used in many applications. PSLQ was only analyzed theoretically for exact input data, however, when the input data are irrational numbers, they must be approximate ones due to the finite precision of the computer. When the algorithm takes empirical data (inexact data with error bounded) instead of exact real numbers as its input, how do we theoretically ensure the output of the algorithm to be an exact integer relation? In this paper, we investigate the PSLQ algorithm for empirical data as its input. Firstly, we give a termination condition for this case. Secondly, we analyze a perturbation on the hyperplane matrix constructed from the input data and hence disclose a relationship between the accuracy of the input data and the output quality (an upper bound on the absolute value of the inner product of the exact data and the computed integer relation), which naturally leads to an error control strategy for PSLQ. Further, we analyze the complexity bound of the PSLQ algorithm for empirical data. Examples on transcendental numbers and algebraic numbers show the meaningfulness of our error control strategy. |
| 资助项目 | NNSF (China)[11471307] ; NNSF (China)[11771421] ; NNSF (China)[11671377] ; NNSF (China)[61572024] ; NNSF (China)[11501540] ; CAS Light of West China Program and Youth Innovation Promotion Association of CAS ; Chongqing Research Program[cstc2015jcyjys40001] ; Chongqing Research Program[KJ1705121] ; CAS Research Program of Frontier Sciences[QYZDB-SSW-SYS026] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000457012400016 |
| 出版者 | AMER MATHEMATICAL SOC |
| 源URL | [http://119.78.100.138/handle/2HOD01W0/7314]  |
| 专题 | 自动推理与认知研究中心 |
| 通讯作者 | Feng, Yong |
| 作者单位 | Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Chongqing Key Lab Automated Reasoning & Cognit, Chongqing 400714, Peoples R China |
| 推荐引用方式 GB/T 7714 | Feng, Yong,Chen, Jingwei,Wu, Wenyuan. THE PSLQ ALGORITHM FOR EMPIRICAL DATA[J]. MATHEMATICS OF COMPUTATION,2019,88(317):1479-1501. |
| APA | Feng, Yong,Chen, Jingwei,&Wu, Wenyuan.(2019).THE PSLQ ALGORITHM FOR EMPIRICAL DATA.MATHEMATICS OF COMPUTATION,88(317),1479-1501. |
| MLA | Feng, Yong,et al."THE PSLQ ALGORITHM FOR EMPIRICAL DATA".MATHEMATICS OF COMPUTATION 88.317(2019):1479-1501. |
入库方式： OAI收割
来源：重庆绿色智能技术研究院
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