We consider interpolation problems for smooth stationary Gaussian processes and functions from Sobolev classes. These problems are shown to be closely related. Much attention is paid to spline-based interpolation methods. In particular, we prove that splines are limiting optimal interpolations of stationary Gaussian processes with special spectral densities. Based on this analogy, we propose a simple method for controlling accuracy of spline interpolation.
Problems of Information Transmission – Springer Journals
Published: Jul 13, 2013
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