Abstract
The paper presents new upper and lower bounds for the Perron root of a nonnegative matrix in terms of the simple circuits of length not exceeding k and the simple paths of length k, 1 ≤ k ≤ n, in the directed graph of the matrix. For each k, 1 ≤ k ≤ n, these bounds are intermediate between the circuit bounds and the path-dependent bounds suggested previously, and for k = 1 and k = n they reduce to the corresponding path-dependent bounds and the circuit bounds, respectively. Bibliography: 5 titles.
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References
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 69–93.
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Kolotilina, L.Y. Bounds and inequalities for the Perron root of a nonnegative matrix. III. Bounds dependent on simple paths and circuits. J Math Sci 137, 4801–4814 (2006). https://doi.org/10.1007/s10958-006-0279-3
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DOI: https://doi.org/10.1007/s10958-006-0279-3