AAA interpolation of equispaced data

Abstract We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced samples. Although it is always better to approximate large numbers of samples if they are available, whether not, this often performs impressively even when the sampling grid coarse. In most cases gives more accurate approximations than other methods. support claim with review and discussion nine classes existing methods in light general properties theory well “impossibility theorem” approximation. make careful use numerical experiments, which summarized sequence figures. Among our new contributions observation, Fig. 7, that such polynomial least-squares Fourier extension may be either exponentially unstable, less stable, depending on implementation.