  The main contribution of this paper is twofold: On the one hand, a general
framework for performing Hermite interpolation on Riemannian manifolds is
presented. The method is applicable, if algorithms for the associated
Riemannian exponential and logarithm mappings are available. This includes many
of the matrix manifolds that arise in practical Riemannian computing
application such as data analysis and signal processing, computer vision and
image processing, structured matrix optimization problems and model reduction.
  On the other hand, we expose a natural relation between data processing
errors and the sectional curvature of the manifold in question. This provides
general error bounds for manifold data processing methods that rely on
Riemannian normal coordinates.
  Numerical experiments are conducted for the compact Stiefel manifold of
rectangular column-orthogonal matrices. As use cases, we compute Hermite
interpolation curves for orthogonal matrix factorizations such as the singular
value decomposition and the QR-decomposition.
