Asymptotic estimations of a perturbed symmetric eigenproblem

被引：0
|
作者：
Gissler, Armand [1 ]
Auger, Anne [1 ]
Hansen, Nikolaus [1 ]
机构：
[1] Ecole Polytech, Inst Polytech Paris, CNRS, CMAP, F-91120 Palaiseau, France
来源：
APPLIED MATHEMATICS LETTERS | 2024年 / 150卷
关键词：
Perturbation of symmetric matrices; Estimation of eigenvectors; INVARIANT SUBSPACES; EIGENVALUES; BOUNDS; PERTURBATIONS; EIGENVECTORS; ADAPTATION;
D O I：
10.1016/j.aml.2023.108951
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：5
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