A relaxation scheme for computation of the joint spectral radius of matrix sets

TL;DR

This paper introduces an iterative method to numerically compute the joint spectral radius and construct Barabanov norms for irreducible matrix sets, advancing the computational techniques in spectral radius analysis.

Contribution

It presents a novel iteration scheme that simultaneously computes the joint spectral radius and constructs Barabanov norms for irreducible matrix sets.

Findings

Successfully computes the joint spectral radius for matrix sets.

Provides a method to construct Barabanov norms numerically.

Enhances computational efficiency in spectral radius calculations.

Abstract

The problem of computation of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In the paper an iteration procedure is considered that allows to build numerically Barabanov norms for the irreducible matrix sets and simultaneously to compute the joint spectral radius of these sets.