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By Froberg R.

ISBN-10: 0471974420

ISBN-13: 9780471974420

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D. Buhmann and A. Iserles, pp. 133-144. Cambridge University Press, Cambridge. Estrada, R. (1998). Regularization of distributions. Int. J. Math. Math. , 21, 625-636. Fasshauer, G. (1999). Solving differential equations with radial basis functions: multilevel methods and smoothing. Technical Report, IIT Chicago. C. D. (1998). Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions. DAMTP Technical Report, Univ. Cambridge. C. D. (1999). Krylov subspace methods for radial basis function interpolation.

14, 429-438. J. (1998b). On the error in surface spline interpolation of a compactly supported function. Manuscript, Univ. Kuwait. S. (1982). The Theory of Generalised Functions. Cambridge University Press, Cambridge. , Ragozin, D. and Sun, X. (1999). A simple approach to the variational theory for interpolation on spheres. In Approximation Theory Bommerholz 1998, ed. D. Buhmann, M. Felten, D. W. Miiller. Birkhauser, Basel. A. (1986). Interpolation of scattered data: distance matrices and conditionally positive definite functions.

The semi-inner product (•, •) is still the one associated with || • ||0. It turns out in practice that this method often provides excellent accuracy with fewer than ten iterations. Another approach to the iterative approximation and refinement of the radial basis function interpolants is that of fast multipole methods. We briefly outline these here. This is explained in detail in Buhmann (2000). However they are sufficiently important that we must, at least, outline the essentials. These algorithms are based on analytic expansions of the underlying radial functions for large argument (see Greengard and Rokhlin (1987)).

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An introduction to Grobner bases by Froberg R.


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