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FilomatVolume 37, Issue 30, 2023, Pages 10395-10413

Algorithms for computing the optimal Geršgorin-type localizations(Article)(Open Access)

  • Milićević, S.,
  • Kostić, V.R.
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  • aDepartment for Applied fundamental disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21000, Serbia
  • bIstituto Italiano di Tecnologia, Via Melen, 83, Genova, 16152, Italy
  • cDepartment of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia

Abstract

In this paper we provide novel algorithms for computing the minimal Geršgorin set for the localizations of eigenvalues. Two strategies for curve tracing are considered: predictor-corrector and triangular grid approximation. We combine these two strategies with two characterizations (explicit and implicit) of the Minimal Geršgorin set to obtain four new numerical algorithms. We show that these algorithms significantly decrease computational complexity, especially for matrices of large size, and compare them on matrices that arise in practically important eigenvalue problems. © 2023, University of Nis. All rights reserved.

Author keywords

eigenvalue localizationminimal Geršgorin setpredictor-corrector methodtriangular grid

Funding details

Funding sponsor Funding number Acronym
174019

  • 1

    The work of S. Milicevi\u0107 and V. R. Kosti\u0107 has been partially supported by the Ministry of Science, Research Grant 174019, Provincial Secretariat for Science of Vojvodina, Research Grants 1136, 1850 and 2010.

  • 2

    2020 Mathematics Subject Classification. Primary 65F15; Secondary 15A18 Keywords. eigenvalue localization, minimal Gers\u02C7gorin set, predictor-corrector method, triangular grid Received: 05 June 2021; Accepted: 10 June 2023 Communicated by Marko Petkovi\u0107 Research supported the Ministry of Science, Research Grant 174019, Provincial Secretariat for Science of Vojvodina, Research Grants 1136, 1850 and 2010. Email addresses: [email protected] (S. Mili\u0107evi\u0107), [email protected], [email protected] (V. R. Kosti\u0107)

  • ISSN: 03545180
  • Source Type: Journal
  • Original language: English
  • DOI: 10.2298/FIL2330395M
  • Document Type: Article
  • Publisher: University of Nis


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