Abstract:

In this paper we study exponential tractability of multivariate $\mathbb{L}_{\infty}$-approximation for weighted Korobov spaces in the worst case setting. We consider all algorithms that use the class $\Lambda^{\text{all}}$ of all linear functionals and the class $\Lambda^{\text{std}}$ of only function evaluations as information. We give matching necessary and sufficient conditions for notions of EC-quasi-polynomial tractability and EC-uniform weak tractability which have not been discussed before in terms of two weight parameters of the problem.

Key words: Exponential convergence tractability, Korobov spaces, Worst case setting, Multivariate $\mathbb{L}_{\infty}$ -approximation