In this paper we give an estimate of the upper and lower bounds on the spectral radius of a nonnegative matrix and proved this theorems,it has improved accurary of the spectral radius estimate. In addition,the validity and precision of these estimation are tested.

Nonnegative matrix;Spectral radius;Estimation

[1] D. Cao. Bounds on eigenvalues and chromatic number. Linear Algebra Appl., 1998, 270: 1-13. [2] R.A. Brualdi and H.J. Ryser. Combinatorial Matrix Theory. Cambridge University Press, New York, 1991, 53-78. [3] Roger A. Horn, Charles R. Johnson. Matrix Analysis. [4] Yin Jianhong. New bounds for the largest eigenvalue of nonnegative matrices. Numerical Computation and Computer Application, 2002(4): 292-295. [5] Tan Xueyuan. Estimates of the spectral radius and separability of nonnegative matrices. Journal of Nanjing Normal University, 2004(1): 24-27. [6] Huang Tingzhu, Yang Chuansheng. Special Matrix Analysis and Applications. Beijing: Science and Technology Press, 2007. [7] Li Liang, Huang Tingzhu. Estimates of the spectral radius of nonnegative irreducible matrices. Acta Mathematicae Applicatae Sinica, 2008(4): 271-277. [8] Cheng Yunpeng (Ed.). Matrix Theory (2nd Edition). Xibei University of Technology, 2003.

DOI： https://doi.org/10.62639/sspjinss10.20250201

Published： 2025