Trigonometric mollification

An automatic method for data smoothing and numerical differentiation, based on mollification techniques, trigonometric interpolation and the principle of generalized cross validation is presented. With data measured at a discrete set of equidistant points in a given interval, the method allows for the approximate recovery of the function and its first derivative on the entire domain. The trigonometric mollification algorithm provides a functional representation for the mollified computed approximations that guarantees good fitting near the endpoints of the interval and the usage of small values of the regularization parameters -radii of mollification- if necessary. These parameters are chosen automatically although no information about the noise distribution is assumed. Error estimates are included together with several numerical examples of interest.