Lp error estimates for approximation by Sobolev splines and Wendland functions on ℝd

摘要

It is known that a Green';s function-type condition may be used to derive rates for approximation by radial basis functions (RBFs). In this paper, we introduce a method for obtaining rates for approximation by functions which can be convolved with a finite Borel measure to form a Green';s function. Following a description of the method, rates will be found for two classes of RBFs. Specifically, rates will be found for the Sobolev splines, which are Green';s functions, and the perturbation technique will then be employed to determine rates for approximation by Wendland functions.

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