Spectral radius of a nonnegative matrix: from rome to indy
type: Item
instance of: scholarly article
title: Spectral radius of a nonnegative matrix: from rome to indy
zbMATH Open document ID: 1291.37023
DOI: 10.1090/S0002-9939-2013-11846-0
author: Michał Misiurewicz
published in: Proceedings of the American Mathematical Society
publication date: 2013-09-04T00:00:00Z
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 6204567
zbMATH Keywords: rome method
zbMATH Keywords: indy method
zbMATH Keywords: spectral radius
zbMATH Keywords: topological entropy
zbMATH Keywords: non-negative matrix
MaRDI profile type: Publication
cites work: Q4492673
cites work: Q3893024
cites work: Spectra of digraphs
cites work: Q4485695
cites work: Q3931654
full work available at URL: s0002-9939-2013-11846-0
OpenAlex ID: W2009170848
review text: The ``rome'' method was invented in 1980, by \textit{L. Block} et al. [Lect. Notes Math. 819, 18--34 (1980; Zbl 0447.58028)], as a means of calculating the spectral radius of square, non-negative matrices. This was then used to calculate the topological entropy of related dynamical systems as the logarithm of the spectral radius. The rome method was used to avoid certain difficulties that arise in the computation of the spectral radius. The idea is to find a small rome -- a set of vertices such that all infinite paths pass through. The author introduces the ``indy'' method, generalizing the rome method, and allowing the calculation in more general situations, for example, when most of the diagonal entries of the matrix are positive. In the indy method, power series replace the polymomials that arise in the rome method, and there is no restriction on the set of vertices allowed.
reviewed by: Geoffrey R. Goodson
description: scientific article; zbMATH DE number 6204567