Joint Spectral Characteristics of Matrices: A Conic Programming Approach
Vladimir Yu. Protasov, Raphaël M. Jungers, Vincent D. Blondel · SIAM Journal on Matrix Analysis and Applications · 2010
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.