Splines and Stationary Gaussian Processes
Golubev Y., Krymova E.
Proc. of the conf. "Information Technologies and Systems". 2012.
Splines are very popular in function interpolation thanks to their robustness and fast computational algorithms. In this talk, it is shown that splines are closely related to the interpolation of stationary Gaussian processes. This fact permits to predict the error of spline interpolation and to compute it very fast. It is shown also that splines are nearly optimal with respect to the minimax interpolation of smooth Gaussian processes and functions from Sobolev’s ball.