Local Approximation on Manifolds Using Radial Functions and Polynomials
Abstract
The main focus of this paper is to give error estimates for interpolation on compact homogeneous manifolds, the sphere being an example of such a manifold. The notion of a radial function on the sphere is generalised to that of a spherical kernel on a compact homogeneous manifold. Reproducing kernel Hilbert space techniques are used to generate a pointwise error estimate for spherical kernel interpolation using a positive definite kernel. By exploiting the nice scaling properties of Lagrange polynomials in the tangent space, the error estimate is bounded above by a power of the point separation, recovering, in particular, the convergence rates for radial approximation on spheres.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP011997
Entities
People
- David L. Ragozin
- Jeremy Levesley
Organizations
- University of Washington