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

Nakatsukasa, Yuji (2011) Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric. Mathematics of Computation, 80 (276). pp. 2127-2142. ISSN 1088-6842(e)

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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.

Item Type:	Article
Uncontrolled Keywords:	Gerschgorin's theorem, generalized eigenvalue problem, Euclidean metric, forward error analysis
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Yuji Nakatsukasa
Date Deposited:	19 Dec 2011
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1740

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