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This paper is concerned with approximation properties of linear combinations of scattered translates of the thin-plate spline radial basis function | · | 2 log | · | where the translates are taken in the unit disc D in R 2. We show that the Lp approximation order for this kind of approximation is 2 + 1/p (for sufficiently smooth functions), which matches… (More)

It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface… (More)

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of N scattered sites, the standard basis for such a space utilizes N globally supported kernels; computing with it is… (More)