D. Goldstein, Holon Institute of Technology, Holon 58102, Israel; email: dmitryg@hit.ac.il
I. Goldstein, Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel; email: ilyago@bgu.ac.il
Abstract/Résumé:
We prove certain probabilistic inequalities for long matrix products generated by a pair of \(2\times 2\) matrices. Our main tool is the so-called Goldstein-Schlag avalanche principle.
Nous prouvons certaines inégalités probabilistes concernant les longs produits de matrices générés par une paire de matrices \(2\times 2\). Notre objectif principal concerne le principe d’avalanche, énoncé par Goldstein et Schlag.
D. Goldstein, Holon Institute of Technology, Holon 58102, Israel; email: dmitryg@hit.ac.il
I. Goldstein, Department of Mathematics, Ben-Gurion University, P. O. Box 653 Beer-Sheva 84105, Israel; email: ilyago@bgu.ac.il
Abstract/Résumé:
The averaged joint spectral radius (AJSR) is defined. By using the avalanche principle we develop an effective algorithm to compute the averaged joint spectral radius for a pair of \(2\times2\) matrices.
Nous introduisons la notion de rayon spectral moyen d’un ensemble fini de matrices. En utilisant le principe d’avalanche, nous développons un algorithme efficace pour calculer le rayon spectral moyen d’une paire de matrices de tailles \(2\times2\).
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