Abstract
In this paper we present a new method of obtaining near-optimal points sets for interpolation by Gaussian radial basis functions networks. The method is based on minimizing the maximal value of the power function. The power function provides an upper bound on the local RBF interpolation error. We use Latin hypercube designs and a space-filling curve based space-filling designs as starting points for the optimization procedure. We restrict our attention to 1-D and 2-D interpolation problems. Finally, we provide results of several numerical experiments. We compare the performance of this new method with the method of [6].
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Bazan, M., Skubalska-Rafajłowicz, E. (2013). A New Method of Centers Location in Gaussian RBF Interpolation Networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_2
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