Subset selection for matrices with fixed blocks | |
Xie, Jiaxin3; Xu, Zhiqiang1,2 | |
刊名 | ISRAEL JOURNAL OF MATHEMATICS |
2021-07-02 | |
页码 | 26 |
ISSN号 | 0021-2172 |
DOI | 10.1007/s11856-021-2171-8 |
英文摘要 | Subset selection for matrices is the task of extracting a column sub-matrix from a given matrix B is an element of DOUBLE-STRUCK CAPITAL R-nxm with m > n such that the pseudoinverse of the sampled matrix has as small Frobenius or spectral norm as possible. In this paper, we consider a more general problem of subset selection for matrices that allows a block to be fixed at the beginning. Under this setting, we provide a deterministic method for selecting a column submatrix from B. We also present a bound for both the Frobenius and spectral norms of the pseudoinverse of the sampled matrix, showing that the bound is asymptotically optimal. The main technology for proving this result is the interlacing families of polynomials developed by Marcus, Spielman and Srivastava. This idea also results in a deterministic greedy selection algorithm that produces the sub-matrix promised by our result. |
资助项目 | Beijing Natural Science Foundation[Z180002] ; NSFC[11688101] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | HEBREW UNIV MAGNES PRESS |
WOS记录号 | WOS:000669309600009 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58872] |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Xie, Jiaxin |
作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Compuat Math, Acad Math & Syst Sci, Beijing 100091, Peoples R China 3.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China |
推荐引用方式 GB/T 7714 | Xie, Jiaxin,Xu, Zhiqiang. Subset selection for matrices with fixed blocks[J]. ISRAEL JOURNAL OF MATHEMATICS,2021:26. |
APA | Xie, Jiaxin,&Xu, Zhiqiang.(2021).Subset selection for matrices with fixed blocks.ISRAEL JOURNAL OF MATHEMATICS,26. |
MLA | Xie, Jiaxin,et al."Subset selection for matrices with fixed blocks".ISRAEL JOURNAL OF MATHEMATICS (2021):26. |
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