Information-based complexity
Open problems for tractability of multivariate integration
Journal of Complexity
Multivariate integration inC∞([0,1]d) is not strongly tractable
Journal of Complexity
Sampling numbers and function spaces
Journal of Complexity
Widths of embeddings in function spaces
Journal of Complexity
Approximation of infinitely differentiable multivariate functions is intractable
Journal of Complexity
Journal of Complexity
Tractability results for weighted Banach spaces of smooth functions
Journal of Complexity
Approximation numbers of Sobolev embeddings-Sharp constants and tractability
Journal of Complexity
The curse of dimensionality for numerical integration of smooth functions II
Journal of Complexity
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We comment on recent results in the field of information based complexity, which state (in a number of different settings), that the approximation of infinitely differentiable functions is intractable and suffers from the curse of dimensionality. We show that renorming the space of infinitely differentiable functions in a suitable way allows weakly tractable uniform approximation by using only function values. Moreover, the approximating algorithm is based on a simple application of Taylor's expansion about the center of the unit cube. We discuss also the approximation on the Euclidean ball and the approximation in the L"1-norm.