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Perturbations of Jordan matrices

Davies, E. B. and Hager, Mildred LU (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.
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author
organization
publishing date
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
2009-05-08 15:56:09
date last changed
2017-10-01 03:53:54
@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},
  keyword      = {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},
  volume       = {156},
  year         = {2009},
}