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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On perturbations of matrix pencils with real spectra, a revisit


Author: Ren-Cang Li
Journal: Math. Comp. 72 (2003), 715-728
MSC (2000): Primary 15A22, 15A42, 65F15
Published electronically: May 16, 2002
MathSciNet review: 1954964
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Abstract: This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.


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Additional Information

Ren-Cang Li
Affiliation: Department of Mathematics, University of Kentucky, Lexington, KY 40506
Email: rcli@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01449-7
PII: S 0025-5718(02)01449-7
Keywords: Diagonalizable matrix pencil, definite pencil, real spectrum, unitarily invariant norm, perturbation bound
Received by editor(s): January 10, 2001
Received by editor(s) in revised form: August 24, 2001
Published electronically: May 16, 2002
Additional Notes: This work was supported in part by the National Science Foundation under Grant No. ACI-9721388 and by the National Science Foundation CAREER award under Grant No. CCR-9875201.
Article copyright: © Copyright 2002 American Mathematical Society