Upper and Lower Bounds for Matrix Discrepancy
文献类型：期刊论文
| 作者 | Xie, Jiaxin2; Xu, Zhiqiang1,3; Zhu, Ziheng1,3 |
| 刊名 | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 2022-12-01 |
| 卷号 | 28期号:6页码:23 |
| 关键词 | Matrix discrepancy Tight frame Interlacing polynomials Kadison-Singer problem |
| ISSN号 | 1069-5869 |
| DOI | 10.1007/s00041-022-09976-w |
| 英文摘要 | The aim of this paper is to study the matrix discrepancy problem. Assume that xi(1), ..., xi(n) are independent scalar random variables with finite support and u(1), ..., u(n) is an element of C-d. Let C-0 be the minimal constant for which the following holds: Disc(u(1)u(1)*,..., u(n)u(n)* ;xi(1), ..., xi(n)) := min(epsilon 1 subset of S1, ..., epsilon n subset of Sn) parallel to Sigma(n)(i=1) E[xi(i)]u(i) u(i)* - Sigma(n)(i=1) epsilon(i)u(i)u(i)*parallel to <= C-0.sigma, where sigma(2) = parallel to Sigma(n)(i=1) Var [xi(i)] (u(i)u(i)*)(2)parallel to and S-j denotes the support of xi(j), j = 1, ..., n. Motivated by the technology developed by Bownik, Casazza, Marcus, and Speegle [7], we prove C-0 <= 3. This improves Kyng, Luh and Song's method with which C-0 <= 4 [21]. For the case where {u(i)}(i=1)(n) subset of C-d is a unit-norm tight frame with n <= 2d - 1 and xi(1), ..., xi(n) are independent Rademacher random variables, we present the exact value of Disc (u(1)u(1)*, ..., u(n)u(n)* ;xi(1), ..., xi(n)) = root n/d.sigma, which implies C-0 >= root 2. |
| 资助项目 | National Science Fund for Distinguished Young Scholars[12025108] ; NSFC[12001026] ; NSFC[12071019] ; NSFC[12021001] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000870331200002 |
| 出版者 | SPRINGER BIRKHAUSER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60737]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Xu, Zhiqiang |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Beihang Univ, Sch Math Sci, LMIB Minist Educ, Beijing 100191, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xie, Jiaxin,Xu, Zhiqiang,Zhu, Ziheng. Upper and Lower Bounds for Matrix Discrepancy[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,2022,28(6):23. |
| APA | Xie, Jiaxin,Xu, Zhiqiang,&Zhu, Ziheng.(2022).Upper and Lower Bounds for Matrix Discrepancy.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,28(6),23. |
| MLA | Xie, Jiaxin,et al."Upper and Lower Bounds for Matrix Discrepancy".JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 28.6(2022):23. |
入库方式： OAI收割
来源：数学与系统科学研究院
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