Computation of joint spectral radius for network model associated with rank-one matrix set

Authors:
Jun Liu;Mingqing Xiao
Affiliations:
Department of Mathematics, Southern Illinois University, Carbondale, IL;Department of Mathematics, Southern Illinois University, Carbondale, IL
Venue:
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Year:
2012

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Abstract

In the paper, we prove that any finite set of rank-one matrices has the finiteness property by making use of (invariant) extremal norm. An explicit formula for the computation of joint/generalized spectral radius of such type of matrix sets is derived. Several numerical examples from current literature are provided to illustrate our theoretical conclusion.