The goal of this paper is to construct %discuss the concept of data--independent optimal point sets for interpolation by radial basis functions. The interpolation points are chosen to be uniformly good % Our approach concentrates on finding good points for all functions from the associated native Hilbert space. To this end we collect various results on the power function, which we use to show that good interpolation points are always uniformly distributed in a certain sense. We also prove convergence of two different greedy algorithms for the construction of near-optimal sets which lead to stable interpolation. Finally, we provide several examples.
Near-Optimal Data-independent Point Locations for Radial Basis Function Interpolation
DE MARCHI, Stefano;
2005-01-01
Abstract
The goal of this paper is to construct %discuss the concept of data--independent optimal point sets for interpolation by radial basis functions. The interpolation points are chosen to be uniformly good % Our approach concentrates on finding good points for all functions from the associated native Hilbert space. To this end we collect various results on the power function, which we use to show that good interpolation points are always uniformly distributed in a certain sense. We also prove convergence of two different greedy algorithms for the construction of near-optimal sets which lead to stable interpolation. Finally, we provide several examples.
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