  Solving the so-called geodesic endpoint problem, i.e., finding a geodesic
that connects two given points on a manifold, is at the basis of virtually all
data processing operations, including averaging, clustering, interpolation and
optimization. On the Stiefel manifold of orthonormal frames, this problem is
computationally involved. A remedy is to use quasi-geodesics as a replacement
for the Riemannian geodesics. Quasi-geodesics feature constant speed and
covariant acceleration with constant (but possibly non-zero) norm. For a
well-known type of quasi-geodesics, we derive a new representation that is
suited for large-scale computations. Moreover, we introduce a new kind of
quasi-geodesics that turns out to be much closer to the Riemannian geodesics.
