Geodesic
On the Construction of Stability Indicators for Nonnegative Matrices
Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 407-418

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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. 
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     author = {V. N. Razzhevaikin and E. E. Tyrtyshnikov},
     title = {On the {Construction} of {Stability} {Indicators} for {Nonnegative} {Matrices}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a7/}
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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/