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Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting. (English) Zbl 1063.41013

Authors’ abstract: 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.

MSC:

41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems
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