Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

Narcowich, Francis; Ward, Joseph; Wendland, Holger

doi:10.1090/S0025-5718-04-01708-9

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
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by Francis J. Narcowich, Joseph D. Ward and Holger Wendland PDF

Math. Comp. 74 (2005), 743-763 Request permission

Abstract:

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. 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). These estimates include situations in which the target function does not belong to the native space of the RBF.

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