An implicit algorithm for computing the minimal Geršgorin set(Article)(Open Access)
- aDepartment for Applied Fundamental Disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21000, Serbia
- bDepartment of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia
- cDepartment of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7594, United States
Abstract
In this paper we present a new algorithm for the computation of the minimal Geršgorin set that can be considered an extension of the results from [5]. While the general approach to calculation of the boundary of the minimal Geršgorin set is kept, the core numerical calculation is changed. Namely, the problem is formulated in such a way that the eigenvalue computations are replaced by LU decompositions, allowing the algorithm to be used for larger matrices more efficiently. To illustrate the benefits, we compare both algorithms on several test matrices. © 2019, University of Nis. All rights reserved.
Funding details
| Funding sponsor | Funding number | Acronym |
|---|---|---|
| 174019 | ||
| Provincial Secretariat for Science and Technological Development | 1136 | PSSTD |
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1
Research supported the Ministry of Science, Research Grant 174019, Provincial Secretariat for Science of Vojvodina, Research Grants 1136, 1850 and 2010. The authors would like to thank the anonymous referees for their constructive remarks that have improved the presentation of our research. The work of S. Mili?evi?, V. R. Kosti? and Lj. Cvetkovi? has been partially supported by the Ministry of Science, Research Grant 174019, Provincial Secretariat for Science of Vojvodina, Research Grants 1136, 1850 and 2010. The work of A. Miedlar has been supported by the Simons Foundation Mathematics and Physical Sciences Collaboration Grant for Mathematicians Award Number: 523985 Eigenvalue Computations in Modern Applications and the University of Kansas New Faculty General Research Fund (NFGRF) Award On generalizing matrix nearness problems: distance to localization.
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2
The authors would like to thank the anonymous referees for their constructive remarks that have improved the presentation of our research. The work of S. Mili\u0107evi\u0107, V. R. Kosti\u0107 and Lj. Cvetkovi\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. The work of A. Miedlar has been supported by the Simons Foundation Mathematics and Physical Sciences Collaboration Grant for Mathematicians Award Number: 523985 Eigenvalue Computations in Modern Applications and the University of Kansas New Faculty General Research Fund (NFGRF) Award On generalizing matrix nearness problems: distance to localization.
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3
2010 Mathematics Subject Classification. Primary 65F15; Secondary 15A18; Keywords. eigenvalue localization, minimal Gers\u02C7goin set, M-matrix, LU decomposition. Received: 09 February 2019; Revised: 29 May 2019; Accepted: 27 September 2019 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] (V. R. Kosti\u0107), [email protected] (Lj. Cvetkovi\u0107), [email protected] (A. Miedlar)
- ISSN: 03545180
- Source Type: Journal
- Original language: English
- DOI: 10.2298/FIL1913229M
- Document Type: Article
- Publisher: University of Nis
© Copyright 2020 Elsevier B.V., All rights reserved.
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