Bounds for the Perron root of positive matrices

作者：Ping Liao · 发表于：Linear and Multilinear Algebra · 年份：2022 · DOI：10.1080/03081087.2022.2081310 · 被引用次数：4 · 研究领域：Matrix Theory and Algorithms、graph theory and CDMA systems、Advanced Optimization Algorithms Research

New bounds for the Perron root ρ(A) of a positive matrix A are proposed. Let R1≥R2≥⋯≥Rn be the row sums of matrix A listed in descending order. We use a pairwise combination method to prove that min1≤k≤j{(1−t)Rk+tRn−k+1}≤ρ(A)≤max1≤k≤j{tRk+(1−t)Rn−k+1},with j=⌈n/2⌉, t=M/(M+m), and M (respectively m) is the maximum (resp. minimum) entry of A. This result improves the well-known bounds Rn≤ρ(A)≤R1, and the same method can also be used to improve several other known bounds.