Optimality of singular vector perturbation under maximum norm

被引：1
|
作者：
Liu, Youming [1 ]
Qi, Xinyu [1 ]
机构：
[1] Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 08期
基金：
中国国家自然科学基金;
关键词：
matrix norm; matrix perturbations; optimality; singular value decomposition; singular vector estimation;
D O I：
10.1002/mma.6249
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Fan, Wang, and Zhong estimate the difference between the singular vectors of a matrix and those of a perturbed matrix in terms of the maximum norm. Their estimations are used effectively to establish the asymptotic properties of robust covariance estimators (see Journal of Machine Learning Research, 2018;18:1-42). In this paper, we give the corresponding lower bound estimates, which show Fan-Wang-Zhong's estimations optimal.
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页码：5010 / 5018
页数：9
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