Polynômes hyperboliques et combinaisons linéaires de certains polynômes hyperboliques

We give some results in the theory of hyperbolic polynomials and we study the hyperbolicity of some linear combinations of hyperbolic polynomials.Note présentée par Philippe G. Ciarlet.     

Image numérique,GMRES et polynômes de Faber

We first show that $6F_n(A)6?2$, where A is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree n corresponding to the numerical range of A. Then we deduce several new error bounds based on the numerical range for GMRES, an iterative method for solving non-Hermitian systems of linear equations. To cite this article: B. Beckermann, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Configurations combinatoires des polynômes fibrés de degré 2

In this Note, we are interested in quadratic fibered polynomials which are skew products of the kind P_c : X × C → X × C, P_c(x, z) = (ƒ(x),z² + c(x)), where X is a compact set, ƒ is a continuous map from X into X, and c is a continuous complex valued function on X considered as a parameter. We construct a compact connected configuration space which gives a combinatorial model of a subset of the parameters space. Then, we explain in which way an abstract configuration can be realized by a quadratic fibered polynomial.     

Sur la compacité des ensembles de Julia des polynômes p-adiques

Let R be a rational function, of degree 2, with complex coefficients. Then the Julia set of R is a closed subset of ¹(), and therefore compact. If one replace by the field _p (completion of an algebraic closure of the field _p of the p-adic numbers), then one can define also a Julia set for a rational function with p-adic coefficients. But as _p is not locally compact, the Julia set may or may not be compact. In this paper, we study the compactness of the Julia set of p-adic polynomials. Mathematics Subject Classification (2000):11S99, 37B99.     

Une propriété caractéristique des polynômes de Laguerre

Sans résumé     

Sur la distance à l'instabilité de polynômes matriciels quadratiques

A bisection method is developed for computing the distance to instability of quadratic matrix polynomials. The computation takes rounding errors into account.     

Biais de l'estimation par polynômes locaux de la fonction de régression d'une suite dépendante

In this Note, we give conditions in terms of the decay of the sequence of strong mixing coefficients in order to control the bias of the local polynomial estimators of the regression function. We show the differences between stationary random sequences and independent, identically distributed sequences. In this case, the computation of biases is highly dependent on the underlying dependence structure, contrarily to the classical Nadaraya—Watson estimator.