Geodesic
On the Construction of Stability Indicators for Nonnegative Matrices
Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 407-418 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Mots-clés : nonnegative matrix
Keywords: stability indicator. 
@article{MZM_2021_109_3_a7,
     author = {V. N. Razzhevaikin and E. E. Tyrtyshnikov},
     title = {On the {Construction} of {Stability} {Indicators} for {Nonnegative} {Matrices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {407--418},
     year = {2021},
     volume = {109},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a7/}
}
TY  - JOUR
AU  - V. N. Razzhevaikin
AU  - E. E. Tyrtyshnikov
TI  - On the Construction of Stability Indicators for Nonnegative Matrices
JO  - Matematičeskie zametki
PY  - 2021
SP  - 407
EP  - 418
VL  - 109
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a7/
LA  - ru
ID  - MZM_2021_109_3_a7
ER  - 
%0 Journal Article
%A V. N. Razzhevaikin
%A E. E. Tyrtyshnikov
%T On the Construction of Stability Indicators for Nonnegative Matrices
%J Matematičeskie zametki
%D 2021
%P 407-418
%V 109
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a7/
%G ru
%F MZM_2021_109_3_a7
V. N. Razzhevaikin; E. E. Tyrtyshnikov. On the Construction of Stability Indicators for Nonnegative Matrices. Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 407-418. http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a7/

[1] A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979 | MR

[2] P. H. Leslie, “On the use of matrices in certain population mathematics”, Biometrica, 33 (1945), 183–212 | DOI | MR

[3] V. N. Razzhevaikin, “Funktsionaly otbora v avtonomnykh modelyakh biologicheskikh sistem s nepreryvnoi vozrastnoi i prostranstvennoi strukturoi”, Zh. vychisl. matem. i matem. fiz., 50:2 (2010), 338–346 | MR

[4] V. N. Razzhevaikin, Analiz modelei dinamiki populyatsii, MFTI, M., 2010

[5] V. Ju. Protasov, D. O. Logofet, “Rank-one corrections of nonnegative matrices, with an applications to matrix population models”, SIAM J. Matrix Anal. Appl., 35:2 (2014), 749–764 | DOI | MR

[6] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989 | MR

[7] D. Uotkins, Osnovy matrichnykh vychislenii, Binom, Laboratoriya znanii, M., 2006 | MR

[8] D. O. Logofet, I. N. Belova, “Neotritsatelnye matritsy kak instrument modelirovaniya dinamiki populyatsii: klassicheskie modeli i sovremennye obobscheniya”, Fundament. i prikl. matem., 13:4 (2007), 145–164 | MR | Zbl