Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius
نویسندگان
چکیده
منابع مشابه
Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets∗
The problem of construction of Barabanov norms for analysis of properties of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In [16, 17] the method of Barabanov norms was the key instrument in disproving the Lagarias-Wang Finiteness Conjecture. The related constructions were essentially based on the study of the geometrical properties of th...
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We show that the joint spectral radius of a set of matrices is strictly increasing as a function of the data in the sense that if a set of matrices is contained in the relative interior of the convex hull of an irreducible set of matrices, then the joint spectral radius of the smaller set is strictly smaller than that of the larger set. This observation has some consequences in the theory of ti...
متن کاملContinuity of the Joint Spectral Radius: Application to Wavelets
Abstract. The joint spectral radius is the extension to two or more matrices of the (ordinary) spectral radius ρ(A) = max |λi(A)| = lim‖A m‖1/m. The extension allows matrix products Πm taken in all orders, so that norms and eigenvalues are difficult to estimate. We show that the limiting process does yield a continuous function of the original matrices—this is their joint spectral radius. Then ...
متن کاملThe generalized spectral radius and extremal norms
The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...
متن کامل2 8 Se p 20 09 An explicit Lipschitz constant for the joint spectral radius ∗
In 2002 F. Wirth has proved that the joint spectral radius of irreducible compact sets of matrices is locally Lipschitz continuous as a function of the matrix set. In the paper, an explicit formula for the related Lipschitz constant is obtained. PACS number 02.10.Ud; 02.10.Yn MSC 2000: 15A18; 15A60
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2018
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.01.042