Elsevier

Journal of Complexity

Volume 25, Issue 4, August 2009, Pages 398-404
Journal of Complexity

Approximation of infinitely differentiable multivariate functions is intractable

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Abstract

We prove that L-approximation of C-functions defined on [0,1]d is intractable and suffers from the curse of dimensionality. This is done by showing that the minimal number of linear functionals needed to obtain an algorithm with worst case error at most ε(0,1) is exponential in d. This holds despite the fact that the rate of convergence is infinite.

Keywords

Tractability
Curse of dimensionality
Rate of convergence
Approximation of smooth functions

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