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A New Gershgorin-type Result for the Localisation of the Spectrum of Matrices

A New Gershgorin-type Result for the Localisation of the Spectrum of Matrices

Anna Dall'Acqua Ulm University Delio Mugnolo FernUniversität Hagen Michael Schelling Ulm University

Mathematische Nachrichten, 2015

Abstract

We present a Gershgorin's type result on the localisation of the spectrum of a matrix. Our method is elementary as it relies upon the method of Schur complements, but it outperforms the one based on the Cassini ovals of Ostrovski and Brauer. Furthermore, it yields estimates that hold without major differences in the cases of both scalar and operator matrices. Several refinements of known results are obtained.

Bibtex

content_copy
@article{schelling2015spectrum,
    title={A New Gershgorin-type Result for the Localisation of the Spectrum of Matrices},
    author={Dall'Acqua, Anna and Mugnolo, Delio and Schelling, Michael},
    year={2015},
    month={7},
    journal={Mathematische Nachrichten},
    volume={288},
    pages={1981-1994},
    issue={17-18},
    doi={10.1002/mana.201400294},
    note={}
}