Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
Rodrigo B. Platte, Lloyd N. Trefethen, Arno B. J. Kuijlaars · SIAM Review · 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.