Summary
It is shown that there is a positive lower bound,c, to the uniform error in any scheme designed to recover all functions of a certain smoothness from their values at a fixed finite set of points. This lower bound is essentially attained by interpolation at the points by splines with canonical knots. Estimates ofc are also given.
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Micchelli, C.A., Rivlin, T.J. & Winograd, S. The optimal recovery of smooth functions. Numer. Math. 26, 191–200 (1976). https://doi.org/10.1007/BF01395972
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DOI: https://doi.org/10.1007/BF01395972