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Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric


Author: Yuji Nakatsukasa
Journal: Math. Comp. 80 (2011), 2127-2142
MSC (2010): Primary 15A22, 15A42, 65F15
DOI: https://doi.org/10.1090/S0025-5718-2011-02482-8
Published electronically: March 30, 2011
MathSciNet review: 2813351
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Abstract: We present Gerschgorin-type eigenvalue inclusion sets applicable to generalized eigenvalue problems. Our sets are defined by circles in the complex plane in the standard Euclidean metric, and are easier to compute than known similar results. As one application we use our results to provide a forward error analysis for a computed eigenvalue of a diagonalizable pencil.


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Additional Information

Yuji Nakatsukasa
Affiliation: Department of Mathematics, University of California, Davis, California 95616
Email: ynakam@math.ucdavis.edu

DOI: https://doi.org/10.1090/S0025-5718-2011-02482-8
Keywords: Gerschgorin’s theorem, generalized eigenvalue problem, Euclidean metric, forward error analysis
Received by editor(s): June 20, 2010
Received by editor(s) in revised form: September 20, 2010
Published electronically: March 30, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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