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Improved error bounds for scattered data interpolation by radial basis functions. (English) Zbl 0917.41011

The author remarks that, in a certain sense, radial basis function techniques could be viewed as a generalization of splines to the multivariate case. First, he presents another approach to the basic facts about native spaces. Then, using these facts in order to consider some smoothness requirements and boundary conditions, he proves that similar to the cubic spline interpolation, the approximation order of scattered data interpolants by radial functions is improved under the new requirements and conditions.

MSC:

41A30 Approximation by other special function classes
41A15 Spline approximation
41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems
65D10 Numerical smoothing, curve fitting
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