Adapting rational approximants for Fourier series to data representation problems (Q1094618)

We consider generalizations of the method of Padé approximants based on Fourier series in a setting where the univariate function to be approximated is known only at equally spaced points. Finding the optimal parameters for the nonlinear trigonometric models is seen to correspond to the solution of a related exponential approximation problem. A complete algorithm is described and is illustrated with a number of examples.