Jean Dieudonné

Bio: Jean Dieudonné is an academic researcher from University of Nice Sophia Antipolis. The author has contributed to research in topics: Cellular algebra & Separable partial differential equation. The author has an hindex of 29, co-authored 48 publications receiving 11519 citations. Previous affiliations of Jean Dieudonné include Institut des Hautes Études Scientifiques.

Éléments de géométrie algébrique

Abstract: © Publications mathématiques de l’I.H.É.S., 1965, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Differentiable dynamical systems

Abstract: This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a homomorphism G→Diff(M) such that the induced map G×M→M is differentiable. Here Diff(M) is the group of all diffeomorphisms of M and a diffeo- morphism is a differentiable map with a differentiable inverse. Everything will be discussed here from the C ∞ or C r point of view. All manifolds maps, etc. will be differentiable (C r , 1 ≦ r ≦ ∞) unless stated otherwise.

Optimization Algorithms on Matrix Manifolds

Abstract: Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

Dynamic Equations on Time Scales: An Introduction with Applications

Abstract: Preface * The Time Scales Calculus * First Order Linear Equations * Second Order Linear Equations * Self-Adjoint Equations * Linear Systems and Higher Order Equations * Dynamic Inequalities * Linear Symplectic Dynamic Systems * Extensions * Solutions to Selected Problems * Bibliography * Index