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Numerische Mathematik

, Volume 26, Issue 2, pp 191–200 | Cite as

The optimal recovery of smooth functions

  • C. A. Micchelli
  • T. J. Rivlin
  • S. Winograd
Article

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.

Keywords

Smooth Function Mathematical Method Optimal Recovery Uniform Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • C. A. Micchelli
    • 1
  • T. J. Rivlin
    • 1
  • S. Winograd
    • 1
  1. 1.Thomas J. Watson Research CenterIBMYorktown HeightsUSA

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