Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples. - Platte, R; Trefethen, L; Kuijlaars, A (2011)
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. © 2011 Society for Industrial and Applied Mathematics.