Jeudi 2 octobre 1997 Séminaire d'analyse numérique et mécanique, Université de Rennes 1

On the joint spectral radius of a family of matrices and applications

Marino ZENNARO

Department of Mathematical Sciences
Trieste University
Piazzale Europa, 1
34127 Trieste Italy

zennaro@univ.trieste.it

We discuss the problem of stability in difference equations, which are written in the form Y_n=(A₀...A_n-1)Y₀. When A_n= A then the stability is ensured if the spectral radius of A is strictly less than 1. In the case of variable coefficients the problem is by far more complicated. Then we need to introduce the notion of joint spectral radius.