On updating the least singular value: a lower bound

CALCOLO ◽  
2003 ◽  
Vol 40 (4) ◽  
pp. 213-229 ◽  
Author(s):  
C. Fassino
Keyword(s):  
Lower Bound ◽  
Singular Value ◽  
Least Singular Value

scholarly journals Optimal lower bound on the least singular value of the shifted Ginibre ensemble

2020 ◽  
Vol 1 (1) ◽  
pp. 101-146
Author(s):  
Giorgio Cipolloni ◽  
László Erdős ◽  
Dominik Schröder
Keyword(s):  
Lower Bound ◽  
Singular Value ◽  
Ginibre Ensemble ◽  
Least Singular Value ◽  
Optimal Lower Bound

A parameterized lower bound for the smallest singular value

2008 ◽  
Vol 17 ◽  
Author(s):  
Wei Zhang ◽  
Zheng-Zhi Han ◽  
Shu-Qian Shen
Keyword(s):  
Lower Bound ◽  
Singular Value ◽  
Smallest Singular Value

On computing bounds for the least singular value of a triangular matrix

1975 ◽  
Vol 15 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Ned Anderson ◽  
Ilkka Karasalo
Keyword(s):  
Triangular Matrix ◽  
Singular Value ◽  
Least Singular Value

scholarly journals A lower bound for the smallest singular value

1992 ◽  
Vol 172 ◽  
pp. 27-32 ◽  
Author(s):  
Y.P. Hong ◽  
C.-T. Pan
Keyword(s):  
Lower Bound ◽  
Singular Value ◽  
Smallest Singular Value

scholarly journals RANDOM MATRICES: THE CIRCULAR LAW

2008 ◽  
Vol 10 (02) ◽  
pp. 261-307 ◽  
Author(s):  
TERENCE TAO ◽  
VAN VU
Keyword(s):  
Strong Convergence ◽  
Random Matrices ◽  
Random Variable ◽  
Singular Value ◽  
Additive Combinatorics ◽  
Sparse Random Matrices ◽  
Circular Law ◽  
Bounded Variance ◽  
Complex Random Variable ◽  
Least Singular Value

Let x be a complex random variable with mean zero and bounded variance σ2. Let Nn be a random matrix of order n with entries being i.i.d. copies of x. Let λ1, …, λn be the eigenvalues of [Formula: see text]. Define the empirical spectral distributionμn of Nn by the formula [Formula: see text] The following well-known conjecture has been open since the 1950's: Circular Law Conjecture: μn converges to the uniform distribution μ∞ over the unit disk as n tends to infinity. We prove this conjecture, with strong convergence, under the slightly stronger assumption that the (2 + η)th-moment of x is bounded, for any η > 0. Our method builds and improves upon earlier work of Girko, Bai, Götze–Tikhomirov, and Pan–Zhou, and also applies for sparse random matrices. The new key ingredient in the paper is a general result about the least singular value of random matrices, which was obtained using tools and ideas from additive combinatorics.

The least singular value of a random square matrix is

2008 ◽  
Vol 346 (15-16) ◽  
pp. 893-896 ◽  
Author(s):  
Mark Rudelson ◽  
Roman Vershynin
Keyword(s):  
Singular Value ◽  
Least Singular Value ◽  
Square Matrix
Sign in / Sign up

Export Citation Format

Share Document