Upper bounds for the spectral radius of matrices having the Perron–Frobenius property

Abstract

Abstract A new upper bound for the spectral radius of matrices having the Perron–Frobenius property is given by considering the position of positive entries. Some examples involving the largest zero of polynomials and the spectral radius of the iterative matrix for the Perron–Frobenius splitting are given to show the superiority of the theoretical result.

Keywords

• Perron–Frobenius property
• Perron–Frobenius splitting
• Polynomials
• Spectral radius