RANK-ONE APPROXIMATION OF JOINT SPECTRAL RADIUS OF FINITE MATRIX FAMILY ∗

In this paper, we show that any finite set of rank-one matrices satisfies the finite- ness property under the linear programming framework. An explicit formula for the computation of joint/generalized spectral radius for this class of matrix family is derived. We further study finite sets of general matrices through constructing rank-one approximations based on singular value decom- position (SVD) and a new characterization of joint/generalized spectral radius is obtained. Several well-known examples as well as their numerical simulations are provided to illustrate the theoretical outcomes.

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