Geodesic
Joint bounds for the Perron roots of nonnegative matrices with applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 30-56

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a finite set $\{A^{(x)}\}_{x\in X}$ of nonnegative matrices, we derive joint upper and lower bounds for the row sums of the matrices $D^{-1}A^{(x)}D$, $x\in X$, where $D$ is a specially chosen nonsingular diagonal matrix. These bounds, depending only on the sparsity patterns of the matrices $A^{(x)}$ and their row sums, are used to obtain joint two-sided bounds for the Perron roots of given nonnegative matrices, joint upper bounds for the spectral radii of given complex matrices, bounds for the joint and lower spectral radii of a matrix set, and conditions sufficient for all convex combinations of given matrices to be Schur stable. 
@article{ZNSL_2006_334_a2,
     author = {Yu. A. Alpin and L. Yu. Kolotilina and N. N. Korneeva},
     title = {Joint bounds for the {Perron} roots of nonnegative matrices with applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--56},
     publisher = {mathdoc},
     volume = {334},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a2/}
}
TY  - JOUR
AU  - Yu. A. Alpin
AU  - L. Yu. Kolotilina
AU  - N. N. Korneeva
TI  - Joint bounds for the Perron roots of nonnegative matrices with applications
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 30
EP  - 56
VL  - 334
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a2/
LA  - ru
ID  - ZNSL_2006_334_a2
ER  - 
%0 Journal Article
%A Yu. A. Alpin
%A L. Yu. Kolotilina
%A N. N. Korneeva
%T Joint bounds for the Perron roots of nonnegative matrices with applications
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 30-56
%V 334
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a2/
%G ru
%F ZNSL_2006_334_a2
Yu. A. Alpin; L. Yu. Kolotilina; N. N. Korneeva. Joint bounds for the Perron roots of nonnegative matrices with applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 30-56. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a2/