Draft of August 17, 2001 Optimal Stability Results for Interpolation by Kernel Functions
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چکیده
This paper proves lower bounds for the eigenvalues of positive definite matrices arising from interpolation of scattered data by positive definite kernels. By comparison with upper bounds for the interpolation error, it turns out that both bounds are asymptotically optimal for sufficiently dense data sets. Applications include interpolation on the sphere, the torus, and general Riemannian manifolds.
منابع مشابه
Armin Iske * Scattered Data Approximation by Positive Definite Kernel Functions
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 ...
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تاریخ انتشار 2009