New bounds for perfect hashing via information theory
European Journal of Combinatorics
Journal of Complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Finite-order weights imply tractability of linear multivariate problems
Journal of Approximation Theory
IEEE Transactions on Information Theory
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In DeVore et al. (2011) [7] we considered smooth functions on [0,1]^N which depend on a much smaller number of variables @? or continuous functions which can be approximated by such functions. We were interested in approximating those functions when we can calculate point values at points of our choice. The number of points we needed for non-adaptive algorithms was higher than that in the adaptive case. In this paper we improve on DeVore et al. (2011) [7] and show that in the non-adaptive case one can use the same number of points (up to a multiplicative constant depending on @?) that we need in the adaptive case.