Joint Spectral Characteristics of Matrices: a Conic Programming Approach

Protasov, Vladimir Y.;Jungers, Raphaël;Blondel, Vincent
(2010) SIAM Journal on Matrix Analysis and Applications — Vol. 31, n° 4, p. 2146-2162 (2010)

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Abstract
We propose a new method to compute the joint spectral radius and the joint spectral subradius of a set of matrices. We first restrict our attention to matrices that leave a cone invariant. The accuracy of our algorithm, depending on geometric properties of the invariant cone, is estimated. We then extend our method to arbitrary sets of matrices by a lifting procedure, and we demonstrate the efficiency of the new algorithm by applying it to several problems in combinatorics, number theory, and discrete mathematics.
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Protasov, V. Y., Jungers, R., & Blondel, V. (2010). Joint Spectral Characteristics of Matrices: a Conic Programming Approach. SIAM Journal on Matrix Analysis and Applications, 31(4), 2146-2162. https://doi.org/10.1137/090759896 (Original work published 2010)