THE PROBABILISTIC ESTIMATES ON THE LARGEST AND SMALLEST q-SINGULAR VALUES OF RANDOM MATRICES

被引：2

作者：

Lai, Ming-Jun ^{[1
]}

Liu, Yang ^{[2
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] Michigan State Univ, Dept Math, E Lansing, MI USA

来源：

MATHEMATICS OF COMPUTATION | 2015年 / 84卷 / 294期

基金：

美国国家科学基金会;

关键词：

Random matrices; probability; pre-Gaussian random variable; generalized singular values; LARGEST EIGENVALUE; INVERTIBILITY; LIMIT; NORM;

D O I：

10.1090/S0025-5718-2014-02895-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the q-singular values of random matrices with pre-Gaussian entries defined in terms of the l(q)-quasinorm with 0 < q <= 1. In this paper, we mainly consider the decay of the lower and upper tail probabilities of the largest q-singular value s(1)((q)), when the number of rows of the matrices becomes very large. Based on the results in probabilistic estimates on the largest q-singular value, we also give probabilistic estimates on the smallest q-singular value for pre-Gaussian random matrices.

引用

页码：1775 / 1794

页数：20

共 31 条

[1] ALANEDELMAN E, 1989, THESIS MIT
[2] [Anonymous], 1996, Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences
[3] A NOTE ON THE LARGEST EIGENVALUE OF A LARGE DIMENSIONAL SAMPLE COVARIANCE-MATRIX
BAI, ZD
SILVERSTEIN, JW
YIN, YQ
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1988, 26 (02) : 166 - 168
[4] NORMS OF RANDOM MATRICES
BENNETT, G
GOODMAN, V
NEWMAN, CM
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1975, 59 (02) : 359 - 365
[5] Buldygin V, 2000, METRIC CHARACTERIZAT, V188
[6] CHARTRAND R, 2009, SIAM J MATRIX ANAL A
[7] EIGENVALUES AND CONDITION NUMBERS OF RANDOM MATRICES
EDELMAN, A
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1988, 9 (04) : 543 - 560
[8] FISHER A, 1922, MATH THEORY PROBABIL, V1
[9] Sparse recovery with pre-Gaussian random matrices
Foucart, Simon
Lai, Ming-Jun
[J]. STUDIA MATHEMATICA, 2010, 200 (01) : 91 - 102
[10] Sparsest solutions of underdetermined linear systems via lq-minimization for 0 < q ≤ 1
Foucart, Simon
Lai, Ming-Jun
[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2009, 26 (03) : 395 - 407

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