TY - JOUR
TI - Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds
AU - Adam, M.
AU - Assimakis, N.
AU - Babouklis, F.
JO - International Journal of Circuits, Systems and Signal Processing
PY - 2020
VL - 14
TODO - null
SP - 423-434
PB - North Atlantic University Union NAUN
SN - null
TODO - 10.46300/9106.2020.14.57
TODO - Linear transformations;  System stability, Discrete time;  Lower bounds;  Non-negative matrix;  Nonnegative systems;  Sharp bounds;  Similarity transformation;  Spectral radii;  Upper Bound, Matrix algebra
TODO - In this paper, a new upper bound and a new lower bound for the spectral radius of a nοnnegative matrix are proved by using similarity transformations. These bounds depend only on the elements of the nonnegative matrix and its row sums and are compared to the well-established upper and lower Frobenius’ bounds. The proposed bounds are always sharper or equal to the Frobenius’ bounds. The conditions under which the new bounds are sharper than the Frobenius' ones are determined. Illustrative examples are also provided in order to highlight the sharpness of the proposed bounds in comparison with the Frobenius’ bounds. An application to linear invariant discrete-time nonnegative systems is given and the stability of the systems is investigated. The proposed bounds are computed with complexity O(n2). © 2020, North Atlantic University Union. All rights reserved.
ER -