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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© 2005 Birkhäuser Verlag Basel/Switzerland
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Davydov, O., Sestini, A., Morandi, R. (2005). Local RBF Approximation for Scattered Data Fitting with Bivariate Splines. In: Mache, D.H., Szabados, J., de Bruin, M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7356-3_8
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