Joint Spectral Characteristics of Matrices: A Conic Programming Approach

We propose a new approach to estimate the joint spectral radius and the joint spectral subradius of an arbitrary set of matrices. We first restrict our attention to matrices that leave a cone invariant. The accuracy of the algorithms, depending on geometric properties of the invariant cone, is estimated. Our algorithms generalize previously known methods which were elaborated for certain particular classes of invariant cones. Then, making use of a lifting procedure, we extend our approach to any set of linear operators, without the common invariant cone assumption. In order to show the good properties of our methods, we consider applications to problems in combinatorics, number theory and discrete mathematics, and improve the state of the art for these problems.

• Type: Journal
• Year: 2010
• Where: SIAMMAX
• Authors: Vladimir Protasov, Raphaël M. Jungers, Vincent D. Blondel
• Keywords: Cone Invariant, Invariant Cone, Invariant Cone Assumption, SIAMMAX 2010