Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 69-93
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L. Yu. Kolotilina. Bounds and inequalities for the Perron root of a nonnegative matrix. III. Bounds dependent on simple paths and circuits. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 69-93. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a7/
@article{ZNSL_2005_323_a7,
author = {L. Yu. Kolotilina},
title = {Bounds and inequalities for the {Perron} root of a nonnegative matrix. {III.~Bounds} dependent on simple paths and circuits},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {69--93},
year = {2005},
volume = {323},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a7/}
}
TY - JOUR
AU - L. Yu. Kolotilina
TI - Bounds and inequalities for the Perron root of a nonnegative matrix. III. Bounds dependent on simple paths and circuits
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2005
SP - 69
EP - 93
VL - 323
UR - http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a7/
LA - ru
ID - ZNSL_2005_323_a7
ER -
%0 Journal Article
%A L. Yu. Kolotilina
%T Bounds and inequalities for the Perron root of a nonnegative matrix. III. Bounds dependent on simple paths and circuits
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 69-93
%V 323
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a7/
%G ru
%F ZNSL_2005_323_a7
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 $k$, $1\le k\le n$, in the directed graph of the matrix. For each $k$, $1\le k\le n$, 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.
