THE PSLQ ALGORITHM FOR EMPIRICAL DATA

doi:10.1090/mcom/3356

	THE PSLQ ALGORITHM FOR EMPIRICAL DATA
	Feng, Yong; Chen, Jingwei; Wu, Wenyuan
刊名	MATHEMATICS OF COMPUTATION
	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
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000457012400016
内容类型	期刊论文
源URL	[http://119.78.100.138/handle/2HOD01W0/7314]
专题	中国科学院重庆绿色智能技术研究院
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.