ON THE HOMOTOPY GROUPS OF STIEFEL MANIFOLD

Bayesian inference on the Stiefel manifold

The Stiefel manifold Vp,d is the space of all d×p orthonormal matrices, and includes the d−1 hypersphere and the space of all orthogonal matrices as special cases. It is often desirable to parametrically or nonparametrically estimate the distribution of variables taking values on this manifold. Unfortunately, the intractable normalizing constant in the likelihood makes Bayesian inference challe...

Note on the convex hull of the Stiefel manifold ∗ Kyle

In this note, we characterize the convex hull of the Stiefel manifold and we find its strong convexity parameter. We also introduce the notion of roundness of a set and show that the Stiefel manifold is round.

On the Implementation of Lie Group Methods on the Stiefel Manifold on the Implementation of Lie Group Methods on the Stiefel Manifold *

There are several applications in which one needs to integrate a system of ODEs whose solution is an n × p matrix with orthonormal columns. In recent papers algorithms of arithmetic complexity order n×p have been proposed. The class of Lie group integrators may seem like a worth while alternative for this class of problems, but it has not been clear how to implement such methods with O(np) comp...

Quadratic programs over the Stiefel manifold

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.

On the Stiefel-whitney Classes of a Manifold. Ii