On Interpolation of Smooth Processes and Functions

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Golubev Y., Krymova E.


Problems of Information Transmission. 2013. V. 49(2). P. 127-148.


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.

Keywords: Approximation, Gaussian Processes


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