Spectral radius of a nonnegative matrix: from rome to indy
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.
scientific article; zbMATH DE number 6204567