Asymptotic estimations of a perturbed symmetric eigenproblem

Fuente: arXiv
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Main Authors: Gissler, Armand, Auger, Anne, Hansen, Nikolaus
Format: Preprint
Published: 2024
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author Gissler, Armand
Auger, Anne
Hansen, Nikolaus
author_facet Gissler, Armand
Auger, Anne
Hansen, Nikolaus
contents We study ill-conditioned positive definite matrices that are disturbed by the sum of $m$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_06983
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Asymptotic estimations of a perturbed symmetric eigenproblem
Gissler, Armand
Auger, Anne
Hansen, Nikolaus
Numerical Analysis
15A42, 15B57
We study ill-conditioned positive definite matrices that are disturbed by the sum of $m$ 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.
title Asymptotic estimations of a perturbed symmetric eigenproblem
topic Numerical Analysis
15A42, 15B57
url https://arxiv.org/abs/2403.06983