Asymptotically optimal designs on compact algebraic manifolds

Abstract

We find t-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree t on the manifold. This generalizes results on the sphere by Bondarenko, Radchenko and Viazovska. Of special interest is the particular case of the Grassmannians where our results improve the bounds that had been proved previously.

References in corpus (3)

• Diameter bounded equal measure partitions of Ahlfors regular metric measure spaces
• Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians
• Sampling of real multivariate polynomials and pluripotential theory

Cited by in corpus (8)

• Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians
• Optimal asymptotic bounds for designs on manifolds
• Points on manifolds with asymptotically optimal covering radius
• On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems
• Cubatures on Grassmannians: moments, dimension reduction, and related topics
• Optimal Monte Carlo integration on closed manifolds
• Chebyshev-type cubature formulas for doubling weights on spheres, balls and simplexes
• Designs related through projective and Hopf maps