Joint Spectral Characteristics of Matrices: A Conic Programming Approach
SIAM Journal on Matrix Analysis and Applications
Computation of joint spectral radius for network model associated with rank-one matrix set
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
An experimental study of approximation algorithms for the joint spectral radius
Numerical Algorithms
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In this paper we consider finite families ${\cal F}$ of real $n\!\times\!n$ matrices. In particular, we focus on the computation of the joint spectral radius $\rho({\cal F})$ via the detection of an extremal norm in the class of complex polytope norms, whose unit balls are balanced complex polytopes with a finite essential system of vertices. Such a finiteness property is very useful in view of the construction of efficient computational algorithms. More precisely, we improve the results obtained in our previous paper [N. Guglielmi, F. Wirth, and M. Zennaro, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 721-743], where we gave some conditions on the family ${\cal F}$ which are sufficient to guarantee the existence of an extremal complex polytope norm. Unfortunately, they exclude unnecessarily many interesting cases of real families. Therefore, here we relax the conditions given in our previous paper in order to provide a more satisfactory treatment of the real case.