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

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

On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations

2016 ◽  
Vol 16 (3) ◽  
pp. 507-522 ◽  
Author(s):  
Yanhui Su ◽  
Lizhen Chen ◽  
Xianjuan Li ◽  
Chuanju Xu
Keyword(s):  
Lower Bound ◽  
Error Estimate ◽  
Spectral Method ◽  
Stokes Equations ◽  
Necessary Condition ◽  
Well Posedness ◽  
Saddle Point Problems ◽  
Numerical Examples ◽  
Lbb Condition ◽  
Optimal Lower Bound

AbstractThe Ladyženskaja–Babuška–Brezzi (LBB) condition is a necessary condition for the well-posedness of discrete saddle point problems stemming from discretizing the Stokes equations. In this paper, we prove the LBB condition and provide the (optimal) lower bound for this condition for the triangular spectral method proposed by L. Chen, J. Shen, and C. Xu in [3]. Then this lower bound is used to derive an error estimate for the pressure. Some numerical examples are provided to confirm the theoretical estimates.

An optimal lower bound for nonregular languages

1994 ◽  
Vol 52 (6) ◽  
pp. 339 ◽  
Author(s):  
A. Bertoni ◽  
Carlo Mereghetti ◽  
Giovanni Pighizzini
Keyword(s):  
Lower Bound ◽  
Optimal Lower Bound

scholarly journals Extreme Values of the Riemann Zeta Function on the 1-Line

2017 ◽  
Vol 2019 (22) ◽  
pp. 6924-6932 ◽  
Author(s):  
Christoph Aistleitner ◽  
Kamalakshya Mahatab ◽  
Marc Munsch
Keyword(s):  
Lower Bound ◽  
Extreme Values ◽  
Mean Square ◽  
Self Similarity ◽  
New Variant ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
The Mean ◽  
Resonator Method ◽  
Optimal Lower Bound

Abstract We prove that there are arbitrarily large values of t such that $|\zeta (1+it)| \geq e^{\gamma } (\log _{2} t +\log _{3} t) + \mathcal{O}(1)$. This essentially matches the prediction for the optimal lower bound in a conjecture of Granville and Soundararajan. Our proof uses a new variant of the “long resonator” method. While earlier implementations of this method crucially relied on a “sparsification” technique to control the mean-square of the resonator function, in the present paper we exploit certain self-similarity properties of a specially designed resonator function.

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
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