  We consider a minimization scheme based on the Householder transport operator
for the Grassman manifold, where a point on the manifold is represented by a m
x n matrix with orthonormal columns. In particular, we consider the case where
m >> n and present a method with asymptotic complexity mn^2. To avoid explicit
parametrization of the manifold we use Householder transforms to move on the
manifold, and present a formulation for simultaneous Householder reflections
for S-orthonormal columns. We compare a quasi-Newton and nonlinear conjugate
gradient implementation adapted to the manifold with a projected nonlinear
conjugate gradient method, and demonstrate that the convergence rate is
significantly improved if the manifold is taken into account when designing the
optimization procedure.
