A hybrid approach to joint spectral radius computation

In this paper we propose a new method to determine the joint spectral radius of a finite set of real matrices by verifying that a given family of candidates actually consists of spectrum maximizing products. Our algorithm aims at constructing a finite set-valued tree according to the approach of Möl...

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Bibliographic Details
Published in:	Linear algebra and its applications
Main Authors:	Mejstrik, Thomas, Reif, Ulrich
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.07.2025
Subjects:	Exact computation Finite tree algorithm Invariant polytope algorithm Joint spectral radius Pseudo spectral radius Pseudo spectral radius Finite tree algorithm 15-04 Joint spectral radius Invariant polytope algorithm 90C90 Exact computation 15A60 15A18
ISSN:	0024-3795
Online Access:	Get full text
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Summary:	In this paper we propose a new method to determine the joint spectral radius of a finite set of real matrices by verifying that a given family of candidates actually consists of spectrum maximizing products. Our algorithm aims at constructing a finite set-valued tree according to the approach of Möller and Reif using a norm that is constructed in the spirit of the invariant polytope algorithm. This combines the broad range of applicability of the first algorithm with the efficiency of the latter. •Novel approach for joint spectral radius computation.•Algorithm remains rigorous.•Algorithm has more general termination guarantees than classical invariant polytope algorithm.
ISSN:	0024-3795
DOI:	10.1016/j.laa.2025.06.024