  Numerical integration and function approximation on compact Riemannian
manifolds based on eigenfunctions of the Laplace-Beltrami operator have been
widely studied in the recent literature. The standard example in numerical
experiments is the Euclidean sphere. Here, we derive numerically feasible
expressions for the approximation schemes on the Grassmannian manifold, and we
present the associated numerical experiments on the Grassmannian. Indeed, our
experiments illustrate and match the corresponding theoretical results in the
literature.
