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Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices

✍ Scribed by Ipsen, I. C. F.; Nadler, B.

Book ID
118211750
Publisher
Society for Industrial and Applied Mathematics
Year
2009
Tongue
English
Weight
180 KB
Volume
31
Category
Article
ISSN
0895-4798

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πŸ“œ SIMILAR VOLUMES

Optimal perturbation bounds for the Herm
Optimal perturbation bounds for the Hermitian eigenvalue problem
✍ Jesse L. Barlow; Ivan Slapničar πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 169 KB

There is now a large literature on structured perturbation bounds for eigenvalue problems of the form where H and M are Hermitian. These results give relative error bounds on the ith eigenvalue, Ξ» i , of the form and bound the error in the ith eigenvector in terms of the relative gap, In general,

A note on eigenvalues of perturbed Hermi
A note on eigenvalues of perturbed Hermitian matrices
✍ Chi-Kwong Li; Ren-Cang Li πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 183 KB

be Hermitian matrices with eigenvalues Ξ» 1 β€’ β€’ β€’ Ξ» k and Ξ» 1 β€’ β€’ β€’ Ξ» k , respectively. Denote by E the spectral norm of the matrix E, and Ξ· the spectral gap between the spectra of H 1 and H 2 . It is shown that , which improves all the existing results. Similar bounds are obtained for singular valu