Localization of Perron roots

AbstractThis paper is concerned with the localization of the Perron root of a nonnegative irreducible matrix A. A new localization method that utilizes the relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complement is presented. The method is efficient because it gives the bounds on ρ(A) only by computing the estimates of the row sums of the generalized Perron complement rather than the generalized Perron complement itself. Several numerical examples are given to illustrate the effectiveness of our method