KMS Of Academy of mathematics and systems sciences, CAS
On Generalizations of p-Sets and their Applications | |
Zhou, Heng1; Xu, Zhiqiang2,3 | |
2019-05-01 | |
Source Publication | NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS |
ISSN | 1004-8979 |
Volume | 12Issue:2Pages:453-466 |
Abstract | The p-set, which is in a simple analytic form, is well distributed in unit cubes. The well-known Weil's exponential sum theorem presents an upper bound of the exponential sum over the p-set. Based on the result, one shows that the p-set performs well in numerical integration, in compressed sensing as well as in uncertainty quantification. However, p-set is somewhat rigid since the cardinality of the p-set is a prime p and the set only depends on the prime number p. The purpose of this paper is to present generalizations of p-sets, say P-d,p(a,epsilon) which is more flexible. Particularly, when a prime number p is given, we have many different choices of the new p-sets. Under the assumption that Goldbach conjecture holds, for any even number m, we present a point set, say L-p,L-q, with cardinality m - 1 by combining two different new p-sets, which overcomes a major bottleneck of the p-set. We also present the upper bounds of the exponential sums over P-d,p(a,epsilon) and L-p,L-q, which imply these sets have many potential applications. |
Keyword | p-set deterministic sampling numerical integral exponential sum |
DOI | 10.4208/nmtma.OA-2017-0145 |
Language | 英语 |
Funding Project | NSFC[91630203] ; NSFC[11331012] ; NSFC[11688101] ; NSFC[61602341] ; National Basic Research Program of China (973 Program)[2015CB856000] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000453759200006 |
Publisher | GLOBAL SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31988 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Zhou, Heng |
Affiliation | 1.Tianjin Polytech Univ, Sch Sci, Tianjin 300160, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
Recommended Citation GB/T 7714 | Zhou, Heng,Xu, Zhiqiang. On Generalizations of p-Sets and their Applications[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2019,12(2):453-466. |
APA | Zhou, Heng,&Xu, Zhiqiang.(2019).On Generalizations of p-Sets and their Applications.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,12(2),453-466. |
MLA | Zhou, Heng,et al."On Generalizations of p-Sets and their Applications".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 12.2(2019):453-466. |
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