Armin Iske * Scattered Data Approximation by Positive Definite Kernel Functions
نویسنده
چکیده
Kernel functions are suitable tools for scattered data interpolation and approximation. We first review basic features of kernel-based multivariate interpolation, before we turn to the construction and the characterization of positive definite kernels and their associated reproducing kernel Hilbert spaces. The optimality of the resulting kernel-based interpolation scheme is shown. Moreover, we analyze the conditioning of the reconstruction problem, before we prove stability estimates for the proposed interpolation method. We finally discuss kernel-based penalized least squares approximation, where we provide more recent results concerning the stability and the convergence of the approximation method.
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