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.