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Subset selection for matrices with fixed blocks

文献类型：期刊论文

作者Xie, Jiaxin3; Xu, Zhiqiang1,2
刊名ISRAEL JOURNAL OF MATHEMATICS
出版日期2021-07-02
页码26
ISSN号0021-2172
DOI10.1007/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
WOS记录号WOS:000669309600009
出版者HEBREW UNIV MAGNES PRESS
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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