Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992.