Geodesic
Bounds and inequalities for the Perron root of a nonnegative matrix. II. Circuit bounds and inequalities
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 60-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper suggests two-sided, upper, and lower circuit bounds for the Perron root of a nonnegative matrix, most of which are derived based on an extension of the monotonicity property of the Perron root established by Fiedler and Pták. 
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L. Yu. Kolotilina. Bounds and inequalities for the Perron root of a nonnegative matrix. II. Circuit bounds and inequalities. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 60-88. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a4/

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