The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices

F Benaych-Georges, RR Nadakuditi - Advances in Mathematics, 2011 - Elsevier
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random
matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and …

[HTML][HTML] The singular values and vectors of low rank perturbations of large rectangular random matrices

F Benaych-Georges, RR Nadakuditi - Journal of Multivariate Analysis, 2012 - Elsevier
In this paper, we consider the singular values and singular vectors of finite, low rank
perturbations of large rectangular random matrices. Specifically, we prove almost sure …

Alternative parametrization of R-matrix theory

CR Brune - Physical Review C, 2002 - APS
An alternative parametrization of R-matrix theory is presented which is mathematically
equivalent to the standard approach, but possesses features that simplify the fitting of …

Outliers in the spectrum of iid matrices with bounded rank perturbations

T Tao - Probability Theory and Related Fields, 2013 - Springer
It is known that if one perturbs a large iid random matrix by a bounded rank error, then the
majority of the eigenvalues will remain distributed according to the circular law. However …

On quantum mean-field models and their quantum annealing

V Bapst, G Semerjian - Journal of Statistical Mechanics: Theory …, 2012 - iopscience.iop.org
This paper deals with fully connected mean-field models of quantum spins with p-body
ferromagnetic interactions and a transverse field. For p= 2 this corresponds to the quantum …

Low rank perturbations of large elliptic random matrices

S O'Rourke, D Renfrew - 2014 - projecteuclid.org
We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations
of large random matrices. In particular, we consider perturbations of elliptic random matrices …

On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications

P Arbenz, GH Golub - SIAM Journal on Matrix Analysis and Applications, 1988 - SIAM
We consider the problem of computing the eigenvalues and vectors of a matrix ̃H=H+D
which is obtained from an indefinite Hermitian low rank modification D of a Hermitian matrix …

Correlation aware sparsified mean estimation using random projection

S Jiang, P Sharma, G Joshi - Advances in Neural …, 2024 - proceedings.neurips.cc
We study the problem of communication-efficient distributed vector mean estimation, which
is a commonly used subroutine in distributed optimization and Federated Learning (FL) …

Solving singular generalized eigenvalue problems. Part II: Projection and augmentation

ME Hochstenbach, C Mehl, B Plestenjak - SIAM Journal on Matrix Analysis …, 2023 - SIAM
Generalized eigenvalue problems involving a singular pencil may be very challenging to
solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing …

Divide and conquer algorithms for the bandsymmetric eigenvalue problem

P Arbenz - Parallel computing, 1992 - Elsevier
Divide and conquer algorithms are formulated for the solution of the eigenvalue problem for
symmetric band matrices. The new algorithms are compared to the traditional solutionspaths …