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We study the approximation of high-dimensional rank one tensors using pointevaluations and consider deterministic as well as randomized algorithms. Weprove that for certain parameters (smoothness and norm of the $r$th derivative)this problem is intractable while for other parameters the problem is tractableand the complexity is only polynomial in the dimension for every fixed$\varepsilon>0$. For randomized algorithms we completely characterize the setof parameters that lead to easy or difficult problems, respectively. In the"difficult" case we modify the class to obtain a tractable problem: The problemgets tractable with a polynomial (in the dimension) complexity if the supportof the function is not too small.

Tractability of the approximation of high-dimensional rank one tensors