Asymptotic estimations of a perturbed symmetric eigenproblem
Numerical Analysis
2024-03-13 v1 Numerical Analysis
Abstract
We study ill-conditioned positive definite matrices that are disturbed by the sum of rank-one matrices of a specific form. We provide estimates for the eigenvalues and eigenvectors. When the condition number of the initial matrix tends to infinity, we bound the values of the coordinates of the eigenvectors of the perturbed matrix. Equivalently, in the coordinate system where the initial matrix is diagonal, we bound the rate of convergence of coordinates that tend to zero.
Cite
@article{arxiv.2403.06983,
title = {Asymptotic estimations of a perturbed symmetric eigenproblem},
author = {Armand Gissler and Anne Auger and Nikolaus Hansen},
journal= {arXiv preprint arXiv:2403.06983},
year = {2024}
}