Geodesic
Bounds and inequalities for the Perron root of a nonnegative matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 77-122

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In this paper, bounds and inequalities for the Perron roots of a nonnegative matrix, extending and complementing the classical theorems of Frobenius and Ostrowski in terms of (deleted) row and column sums, are presented. All the results are derived by using the same approach, based on the monotoncity property of the Perron root. 
@article{ZNSL_2002_284_a5,
     author = {L. Yu. Kolotilina},
     title = {Bounds and inequalities for the {Perron} root of a nonnegative matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--122},
     publisher = {mathdoc},
     volume = {284},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a5/}
}
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L. Yu. Kolotilina. Bounds and inequalities for the Perron root of a nonnegative matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 77-122. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a5/