Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices

Abstract

In this article, we determine upper and lower bounds for the spectral radius of nonnegative matrices. Introducing the notion of average 4-row sum of a nonnegative matrix, we extend various existing formulas for spectral radius bounds. We also refer to their equality cases if the matrix is irreducible, and we present numerical examples to make comparisons among them. Finally, we provide an application to special matrices such as the generalized Fibonacci matrices, which are widely used in applied mathematics and computer science problems. © 2022 Maria Adam and Aikaterini Aretaki, published by De Gruyter.