A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory
Dynamical Systems
2009-06-02 v1 Numerical Analysis
Abstract
We use ergodic theory to prove a quantitative version of a theorem of M. A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a theorem asserting the existence of a continuous invariant splitting for certain matrix cocycles defined over a minimal homeomorphism and having the property that all forward products are uniformly bounded.
Keywords
Cite
@article{arxiv.0906.0260,
title = {A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory},
author = {Ian D. Morris},
journal= {arXiv preprint arXiv:0906.0260},
year = {2009}
}