Information-based complexity
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Multivariate L∞ approximation in the worst case setting over reproducing kernel Hilbert spaces
Journal of Approximation Theory
On the power of standard information for multivariate approximation in the worst case setting
Journal of Approximation Theory
Approximation of infinitely differentiable multivariate functions is intractable
Journal of Complexity
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We study the L"~-approximation problem for weighted Banach spaces of smooth d-variate functions, where d can be arbitrarily large. We consider the worst case error for algorithms that use finitely many pieces of information from different classes. Adaptive algorithms are also allowed. For a scale of Banach spaces we prove necessary and sufficient conditions for tractability in the case of product weights. Furthermore, we show the equivalence of weak tractability with the fact that the problem does not suffer from the curse of dimensionality.