On the sharpness of two-sided bounds for the Perron Root and of the related eigenvalue inclusion sets |
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| Authors: | L.Yu. Kolotilina |
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| Affiliation: | St. Petersburg Branch of the V.A., Steklov Mathematical Institute of the Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russian Federation |
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| Abstract: | The paper considers the sharpness problem for certain two-sided bounds for the Perron root of an irreducible nonnegative matrix. The results obtained are applied to prove the sharpness of the related eigenvalue inclusion sets in classes of matrices with fixed diagonal entries, bounded above deleted absolute row sums, and a partly specified irreducible sparsity pattern. |
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| Keywords: | Nonnegative matrices Perron root Two-sided bounds Directed graph Simple circuits Eigenvalue inclusion sets |
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