Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere

Authors

Edward J. Fuselier, United States Military Academy
Francis J. Narcowich, Texas A & M University - College Station
Joseph D. Ward, Texas A & M University - College Station
Grady Wright, Boise State UniversityFollow

Document Type

Article

Publication Date

10-2009

Abstract

Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R³. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S². In particular, Sobolev-type error estimates are obtained, as well as optimal stability estimates for the associated interpolation matrices. In addition, a Bernstein estimate and an inverse theorem are also derived. Numerical validation of the theoretical results is also given.

Copyright Statement

First published in Mathematics of Computation 78 (268) 2009, published by the American Mathematical Society. DOI: 10.1090/S0025-5718-09-02214-5

Publication Information

Fuselier, Edward J.; Narcowich, Francis J.; Ward, Joseph D.; and Wright, Grady. (2009). "Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere". Mathematics of Computation, 78(268), 2157-2186. https://doi.org/10.1090/S0025-5718-09-02214-5