Asymptotic estimations of a perturbed symmetric eigenproblem
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911793348083712 |
|---|---|
| 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 |