Kunis, Stefan : A note on stability results for scattered data interpolation on Euclidean spheres

Author(s):

Kunis, Stefan

Title:

A note on stability results for scattered data interpolation on Euclidean spheres

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2007

Mathematics Subject Classification:

33C55

[ Spherical harmonics ]

Abstract:

The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the used polynomial degree and the separation distance of the sampling nodes. To this end, we establish a packing argument for well separated sampling nodes and construct strongly localised polynomials on spheres. Numerical results illustrate our theoretical findings.

Keywords:

interpolation, localised polynomials, separation distance, zonal functions

Language:

English

Publication time:

4 / 2007