Abstract
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 liker α 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.
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Communicated by P.J. Laurent
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Levesley, J. Convolution kernels based on thin-plate splines. Numer Algor 10, 401–419 (1995). https://doi.org/10.1007/BF02140777
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DOI: https://doi.org/10.1007/BF02140777