The symplectic Stiefel manifold, denoted by ${Sp}(2p,2n)$, is the set of linear maps between standard spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to well-known $2n\times 2n$ matrices. Optimization problems on ${Sp}(2p,2n)$ find applications in various areas, such as optics, quantum physics, numerical algebra, model order reduction dynamical systems. purpose this paper...

The Kustaanheimo–Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively in studies of the perturbed Kepler problem in celestial mechanics and atomic physics. In contrast to the conventional matrixbased approach, the formulation o...

L’anneau de cohomologie d’un groupe fini, modulo un nombre premier, peut être calculé à l’aide d’un ordinateur, comme l’a montré Carlson. Ici “calculer” signifie trouver une présentation en termes de générateurs et relations, et seul l’anneau (gradué) sous-jacent est en jeu. Nous proposons une méthode pour déterminer certains éléments de structure supplémentaires: classes de Stiefel-Whitney et ...

The main result of this paper is a computation of the motivic cohomology of varieties of n × m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general linear group-scheme with a Tate suspension of a space which is A1-equivalent to projective n− 1-space with a disjoint basepoint.

We characterize the optimal solution of a quadratic program over the Stiefel manifold with an objective function in trace formulation. The result is applied to relaxations of HQAP and MTLS. Finally, we show that strong duality holds for the Lagrangian dual, provided some redundant constraints are added to the primal program. © 2005 Elsevier B.V. All rights reserved.

In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A 2 R mk , B 2 R mp , m p k, we seek the minimum of kA?BQk 2 for all matrices Q 2 R pk , Q T Q = I kk. We introduce a class of relaxation methods for generating minimizing sequences and ooer a geometric interpretation of these methods. Results of numerical experiments illustrating the...

The aim of this paper is to present a unifying view of four SVD-neural-computation techniques found in the scientific literature and to present some theoretical results on their behavior. The considered SVD neural algorithms are shown to arise as Riemannian-gradient flows on double Stiefel manifold and their geometric and dynamical properties are investigated with the help of differential geome...