Accession Number:

ADP011997

Title:

Local Approximation on Manifolds Using Radial Functions and Polynomials

Descriptive Note:

Conference paper

Corporate Author:

WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

2000-01-01

Pagination or Media Count:

10.0

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.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE