Skip to main content
Numerical Linear Algebra with ApplicationsVolume 23, Issue 2, 1 March 2016, Pages 272-290

An algorithm for computing minimal Geršgorin sets(Article)

  Save all to author list
  • aDepartment of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia
  • bInstitut für Mathematik, MA 4-5, Technische Universität Berlin, Strasse des 17. Juni, Berlin, 10625, Germany

Abstract

Summary: The existing algorithms for computing the minimal Geršgorin set are designed for small and medium size (irreducible) matrices and based on Perron root computations coupled with bisection method and sampling techniques. Here, we first discuss the drawbacks of the existing methods and present a new approach based on the modified Newton's method to find zeros of the parameter dependent left-most eigenvalue of a Z-matrix and a special curve tracing procedure. The advantages of the new approach are presented on several test examples that arise in practical applications. Copyright © 2015 John Wiley & Sons, Ltd.

Author keywords

Curve tracingEigenvalue localizationMinimal Geršgorin set
  • ISSN: 10705325
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1002/nla.2024
  • Document Type: Article
  • Publisher: John Wiley and Sons Ltd

  Kostić, V.R.; Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, Serbia;
© Copyright 2016 Elsevier B.V., All rights reserved.

Cited by 1 document

Kostić, V. , Gardašević, D.
On the Geršgorin-type localizations for nonlinear eigenvalue problems
(2018) Applied Mathematics and Computation
View details of this citation
Inform me when this document is cited in Scopus:
Set citation alert Set citation feed
{"topic":{"name":"Eigenvalue; Complementarity Problem; Matrix (Mathematics)","id":32032,"uri":"Topic/32032","prominencePercentile":52.169388,"prominencePercentileString":"52.169","overallScholarlyOutput":0},"dig":"d75d537740167f8bd080a09ccdf7167bc55cd2c5acfa06e6b971d34c0b3da729"}

SciVal Topic Prominence

Topic:
Prominence percentile: