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Advances in Computational Mathematics

, Volume 41, Issue 1, pp 55–75 | Cite as

On general principles of eigenvalue localizations via diagonal dominance

  • V. KostićEmail author
Article

Abstract

This paper suggests a unifying framework for matrix spectra localizations that originate from different generalizations of strictly diagonally dominant matrices. Although a lot of results of this kind have been published over the years, in many papers same properties were proven for every specific localization area using basically the same techniques. For that reason, here, we introduce a concept of DD-type classes of matrices and show how to construct eigenvalue localization sets. For such sets we then prove some general principles and obtain as corollaries many singular results that occur in the literature. Moreover, obtained principles can be used to construct and use novel Geršgorin-like localization areas. To illustrate this, we first prove a new nonsingularity result and then use established principles to obtain the corresponding localization set and its several properties. In addition, some new results on eigenvalue separation lines and upper bounds for spectral radius are obtained, too.

Keywords

Eigenvalues Diagonal dominance Geršgorin’s set H-matrices 

Mathematics Subject Classifications (2010)

65F15 15A18 15A22 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsFaculty of Science, University of Novi SadNovi SadSerbia

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