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Matematicheskie Zametki, 2021, Volume 109, Issue 3, Pages 407–418
DOI: https://doi.org/10.4213/mzm12782 (Mi mzm12782) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Construction of Stability Indicators for Nonnegative Matrices

V. N. Razzhevaikina, E. E. Tyrtyshnikovb

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow
Full-text PDF (495 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm12782
Abstract: Given a square nonnegative matrix $A$, a simple algorithm is suggested for constructing a stability indicator characterizing the localization of its spectrum in the unit disk. Theorems are proved which establish the possibility to use the maximum of $1-\det(I-J)$ over all possible principal submatrices $J$ of $A$ as a suitable indicator and give conditions under which such a maximum can be calculated only over a certain chain of leading principal submatrices. Applied problems that need such constructions and a relationship between the obtained results and similar results established for a number of matrices of special form are considered.
Keywords: nonnegative matrix, stability indicator.
Funding agency Grant number
Russian Science Foundation 19-11-00338
This work was financially supported by the Russian Science Foundation under grant 19-11-00338.
Received: 06.05.2020
Revised: 19.10.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 3, Pages 435–444
DOI: https://doi.org/10.1134/S0001434621030111
Bibliographic databases:
Document Type: Article
UDC: 519.614.2
Language: Russian
Citation: V. N. Razzhevaikin, E. E. Tyrtyshnikov, “On the Construction of Stability Indicators for Nonnegative Matrices”, Mat. Zametki, 109:3 (2021), 407–418; Math. Notes, 109:3 (2021), 435–444
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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