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Local RBF approximation for scattered data fitting with bivariate splines

Davydov, O. and Sestini, A. and Morandi, R. (2005) Local RBF approximation for scattered data fitting with bivariate splines. In: Trends and Applications in Constructive Approximation. International Series of Numerical Mathematics, 151 . Birkhäuser (Springer), Berlin, Germany, pp. 91-102. ISBN 3-7643-7124-2

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In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given.