Continuous and discrete least-squares approximation by radial basis functions on spheres Academic Article uri icon

abstract

  • In this paper we discuss Sobolev bounds on functions that vanish at scattered points on the n-sphere Sn in Rn + 1. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least-squares surface fits via radial basis functions (RBFs). We also address a stabilization or regularization technique known as spline smoothing. © 2006 Elsevier Inc. All rights reserved.

author list (cited authors)

  • Le Gia, Q. T., Narcowich, F. J., Ward, J. D., & Wendland, H.

citation count

  • 34

publication date

  • November 2006