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.
引用
收藏
页码：5010 / 5018
页数：9
相关论文
共 50 条
  • [31] An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction
    Liu, Xin
    Chen, Jing
    Liu, Yongzhu
    Huo, Zhenhua
    Xu, Zhizhen
    Chen, Fajing
    Wang, Jing
    Ma, Yanan
    Han, Yumeng
    ADVANCES IN ATMOSPHERIC SCIENCES, 2024, 41 (03) : 545 - 563
  • [32] Perturbation bounds for diagonalizable matrix eigenvalues under operator norm
    Zhan, Shi-Lin
    PROCEEDINGS OF THE 14TH CONFERENCE OF INTERNATIONAL LINEAR ALGEBRA SOCIETY, 2007, : 407 - 411
  • [33] Vector Perturbation Precoding Under Quantized CSI
    Herath, Sanjeewa P.
    Nguyen, Duy H. N.
    Tho Le-Ngoc
    IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, 2016, 65 (01) : 420 - 427
  • [34] Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces
    Tozoni, SA
    STUDIA MATHEMATICA, 2004, 161 (01) : 71 - 97
  • [35] SINGULAR PERTURBATION APPROACH TO MAXIMUM PRINCIPLE FORMULATION OF VISCOUS INCOMPRESSIBLE FLUID FLOW
    Matsuba, Ikuo
    INTERNATIONAL JOURNAL OF APPLIED MECHANICS, 2010, 2 (03) : 557 - 568
  • [36] SINGULAR PERTURBATION
    COLE, JD
    ADVANCES IN MATHEMATICS, 1975, 16 (03) : 380 - 392
  • [37] WAVE-FORM RELAXATION AND PERTURBATION THEOREM FOR ACCRETIVE-OPERATORS IN THE MAXIMUM NORM
    TAUBERT, K
    WIEDL, W
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1993, 73 (7-8): : T925 - T927
  • [38] Optimality Conditions for Nondifferentiable Vector Optimization Problems under Invexity
    Sun, Hai
    Lin, Ling
    ADVANCES IN INFORMATION TECHNOLOGY AND EDUCATION, PT I, 2011, 201 : 1 - +
  • [39] Effects of Vector Norm Types in Maximum Stiffness Problem of Simple Truss Structures
    Choong, Kook Keong
    Loh, Irene Wee Ling
    Kim, Jae-Yeol
    Kang, Joowon
    JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING, 2009, 8 (02) : 485 - 492
  • [40] Singular-vector perturbation growth in a primitive equation model with moist physics
    Ehrendorfer, M
    Errico, RM
    Raeder, KD
    JOURNAL OF THE ATMOSPHERIC SCIENCES, 1999, 56 (11) : 1627 - 1648
12345