Perturbations of Jordan matrices
(2009) In Journal of Approximation Theory 156(1). p.82-94- Abstract
- We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In the case of random perturbations we obtain explicit estimates which show that as the size of the matrix increases, most of the eigenvalues of the perturbed matrix converge to a certain circle with centre at the origin. In the case of finite rank perturbations we completely determine the spectral asymptotics as the size of the matrix increases. (C) 2008 Elsevier Inc. All fights reserved.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1372178
- author
- Davies, E. B. and Hager, Mildred LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Spectrum, Pseudospectrum, Random matrices, Lidskii, Perturbations, Jordan matrices, Eigenvalues
- in
- Journal of Approximation Theory
- volume
- 156
- issue
- 1
- pages
- 82 - 94
- publisher
- Elsevier
- external identifiers
-
- wos:000263394700004
- scopus:58549094902
- ISSN
- 0021-9045
- DOI
- 10.1016/j.jat.2008.04.021
- language
- English
- LU publication?
- yes
- id
- d5ce451b-3a75-4ace-9eee-1bbb0b1c6a69 (old id 1372178)
- date added to LUP
- 2016-04-01 12:23:37
- date last changed
- 2022-01-27 03:05:27
@article{d5ce451b-3a75-4ace-9eee-1bbb0b1c6a69, abstract = {{We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In the case of random perturbations we obtain explicit estimates which show that as the size of the matrix increases, most of the eigenvalues of the perturbed matrix converge to a certain circle with centre at the origin. In the case of finite rank perturbations we completely determine the spectral asymptotics as the size of the matrix increases. (C) 2008 Elsevier Inc. All fights reserved.}}, author = {{Davies, E. B. and Hager, Mildred}}, issn = {{0021-9045}}, keywords = {{Spectrum; Pseudospectrum; Random matrices; Lidskii; Perturbations; Jordan matrices; Eigenvalues}}, language = {{eng}}, number = {{1}}, pages = {{82--94}}, publisher = {{Elsevier}}, series = {{Journal of Approximation Theory}}, title = {{Perturbations of Jordan matrices}}, url = {{http://dx.doi.org/10.1016/j.jat.2008.04.021}}, doi = {{10.1016/j.jat.2008.04.021}}, volume = {{156}}, year = {{2009}}, }