Algoritmi per il calcolo del raggio spettrale di una famiglia di matrici

ARGOMENTI: Convegni Dottorato

Mercoledi` 30 gennaio 2008 alle ore 15:00, in aula 2BC/30
Cristina VAGNONI (Dottorato in Matematica Computazionale) "Algoritmi per il calcolo del raggio spettrale di una famiglia di matrici"

[Algorithms for the computation of the joint spectral radius]
The asymptotic behaviour of the solutions of a discrete linear dynamical system is related to the spectral radius R of its associated family F; in particular, a system is stable if R <= 1 and there exists an extremal norm for F. In the last decades some algorithms have been proposed in order to find real extremal norms of polytope type in the case of finite families. However, recently it has been observed that it is more useful to consider complex polytope norms. In this talk we show an approach based on the notion of "balanced complex polytopes"; due to the strong increase in complexity of the geometry of such objects, the exposition will be confined to the two-dimensional case. In particular, we give original theoretical results on the geometry of
two-dimensional balanced complex polytopes in order to present two efficient algorithms, one for the geometric representation of a balanced complex polytope and the other the computation of the corresponding complex polytope norm of a vector.

Rif. int. C. Marastoni, T. Vargiolu

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