Abstract
A new multivariate approximation scheme on Rd using scattered translates of the “shifted” surface spline function is developed. The scheme is shown to provide spectral L p -approximation orders with 1 ≤ p ≤ ∞, i.e., approximation orders that depend on the smoothness of the approximands. In addition, it applies to noisy data as well as noiseless data. A numerical example is presented with a comparison between the new scheme and the surface spline interpolation method.
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Communicated by Robert Schaback.
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Yoon, J. Approximation in L p (Rd) from a space spanned by the scattered shifts of a radial basis function. Constr. Approx 17, 227–247 (2001). https://doi.org/10.1007/s003650010033
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DOI: https://doi.org/10.1007/s003650010033