Subset selection for matrices with fixed blocks

doi:10.1007/s11856-021-2171-8

	Subset selection for matrices with fixed blocks
	Xie, Jiaxin 3; Xu, Zhiqiang 1,2
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.