Rank-one Approximation of Joint Spectral Radius of Finite Matrix Family

Details Rank-one Approximation of Joint Spectral Radius of Finite Matrix Family Rank-one Approximation of Joint Spectral Radius of Finite Matrix Family

2011-09-07

arxiv.org/abs/1109.1356v3

Mathematics

Numerical Analysis

Submitted for review on April 23, 2011; This paper has been withdrawn by the author due to a crucial mistake of the proof in S

Scientific paper

In this paper, we show that any finite set of rank-one matrices satisfies the finiteness property under the framework of (invariant) extremal norm. Characterization for the computation of joint/generalized spectral radius for this class of matrix family is derived. Based on that, we further study the joint/generalized spectral radius of finite sets of general matrices through constructing rank-one approximations in terms of singular value decomposition (SVD) and a new characterization of joint/generalized spectral radius is obtained. Several benchmark examples from applications as well as their computational simulations are provided to illustrate the theoretical outcomes.

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