## 2011.115: Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric

2011.115:
Yuji Nakatsukasa
(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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DOI: 10.1090/S0025-5718-2011-02503-2

## 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 |
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Uncontrolled Keywords: | Gerschgorin's theorem, generalized eigenvalue problem, Euclidean metric, forward error analysis |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2011.115 |

Deposited By: | Yuji Nakatsukasa |

Deposited On: | 19 December 2011 |

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