Convolution kernels based on thin-plate splines
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Quasi-interpolation using radial basis functions has become a popular method for constructing approximations to continuous functions in many space dimensions. In this paper we discuss a procedure for generating kernels for quasi-interpolation, using functions which have series expansions involving terms likerα logr. It is shown that such functions are suitable if and only if α is a positive even integer and the spatial dimension is also even.
KeywordsRadial basis functions thin-plate splines convolution kernels
AMS(MOS) subject classification41A30 41A63
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