Hybrid approach to the joint spectral radius computation

TL;DR

This paper introduces a modified invariant polytope algorithm that incorporates ideas from the finite expressible tree algorithm, enhancing its applicability to a broader class of matrix families.

Contribution

It presents a novel hybrid algorithm combining ipa and feta techniques, extending the range of matrices for joint spectral radius computation.

Findings

The new algorithm applies to a wider range of matrix families.

It improves computational efficiency over existing methods.

The approach demonstrates better convergence properties.

Abstract

In this paper we propose a modification to the invariant polytope algorithm (ipa) using ideas of the finite expressible tree algorithm (feta) by M\"oller and Reif. We show that our new feta-flavoured-ipa applies to a wider range of matrix families.