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 ...

Abstract In this paper we construct a family of ternary interpolatory Hermite subdivision schemes order 1 with small support and ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness. Indeed, leaving the binary domain, it is possible ...

We prove new inequalities and equalities for the generalized joint spectral radius (and their essential versions) of Hadamard (Schur) geometric means bounded sets positive kernel operators on Banach function spaces. In case non-negative matrices that define sequences, we obtain additional results. Our results extend several authors appeared relatively recently.

Weighted automata over the tropical semiring Zmax = (Z ∪ {−∞},max,+) are closely related to finitely generated semigroups of matrices over Zmax. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is ...

We provide upper estimates on the spectral radius of a directed graph. In particular we prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.

Acknowledgements I first would like to thank my promotor Vincent Blondel for accepting me as his first Ph.D student, and providing me with a challenging research subject. His constructive comments, his pragmatism and his initiative were essential in the realization of this thesis. Several researchers contributed to this thesis. I would like to especially thank Alexander Vladimirov and Yurii Nes...