Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians
It provides a practical implementation of known theoretical methods for a new manifold type, which is incremental for researchers working on manifold-based numerical methods.
This paper extends numerical integration and function approximation methods based on Laplace-Beltrami eigenfunctions from spheres to Grassmannian manifolds, providing feasible expressions and numerical experiments that confirm theoretical results.
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.