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Advances in Computational MathematicsVolume 35, Issue 2, November 2011, Pages 271-280

A simple generalization of Geršgorin's theorem(Article)

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  • aDepartment of Mathematics and Informatics, Faculty of Science, University of Novi Sad Serbia, 21000 Novi Sad, Serbia
  • bInstitut de Matemàtica Multidisciplinária, Universitat Politècnica de València, Camí de Vera s/n., 46022 València, Spain

Abstract

It is well known that the spectrum of a given matrix A belongs to the Geršgorin set Γ(A), as well as to the Geršgorin set applied to the transpose of A, Γ(AT). So, the spectrum belongs to their intersection. But, if we first intersect i-th Geršgorin disk Γi(A) with the corresponding disk Γi(AT) and then we make union of such intersections, which are, in fact, the smaller disks of each pair, what we get is not an eigenvalue localization area. The question is what should be added in order to catch all the eigenvalues, while, of course, staying within the set Γ(A) ∩ Γ(AT). The answer lies in the appropriate characterization of some subclasses of nonsingular H-matrices. In this paper we give two such characterizations, and then we use them to prove localization areas that answer this question. © 2009 Springer Science+Business Media, LLC.

Author keywords

α-matricesEigenvalue localizationH-matrices

Funding details

Funding sponsor Funding number Acronym
MTM2007-64477
Ministry of Science and Environmental Protection144025
Universitat Politècnica de ValènciaUPV
Provincial Secretariat for Science and Technological Development0708PSSTD

  • 1

    Acknowledgements This work is supported by the agreement of research cooperation between University of Novi Sad (Serbia) and Universitat Politècnica de València (Spain), by Spanish DGI grant MTM2007-64477, by the Provincial Secretariat of Science and Technological Development of Vojvodina, Serbia, grant 0708 and by the Ministry of Science and Environmental Protection of Serbia, grant 144025.

  • ISSN: 10197168
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1007/s10444-009-9143-6
  • Document Type: Article

  Pedroche, F.; Institut de Matemàtica Multidisciplinária, Universitat Politècnica de València, Camí de Vera s/n., Spain;
© Copyright 2011 Elsevier B.V., All rights reserved.

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