Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples

Authors:
Rodrigo B. Platte;Lloyd N. Trefethen;Arno B. J. Kuijlaars
Affiliations:
-;-;arno.kuijlaars@wis.kuleuven.be
Venue:
SIAM Review
Year:
2011

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Abstract

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.