O. Davydov, A. Sestini and R. Morandi, Local RBF approximation for scattered data fitting with bivariate splines, in  "Trends and Applications in Constructive Approximation," (M. G. de Bruin, D. H. Mache, and J.Szabados, Eds.), pp.91--102, ISNM Vol.151, Birkhäuser, 2005.

Abstract: In this paper we continue our earlier research [4] aimed at developing efficient 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, significantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given.

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