ERROR AND STABILITY ESTIMATES FOR SURFACE-DIVERGENCE FREE RBF INTERPOLANTS ON THE SPHERE Academic Article uri icon

abstract

  • Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R 3 mathbb {R}^3 . In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S 2 mathbb {S}^2 . 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.

published proceedings

  • MATHEMATICS OF COMPUTATION

author list (cited authors)

  • Fuselier, E. J., Narcowich, F. J., Ward, J. D., & Wright, G. B.

citation count

  • 13

complete list of authors

  • Fuselier, Edward J||Narcowich, Francis J||Ward, Joseph D||Wright, Grady B

publication date

  • October 2009