Tractability of approximation in the weighted Korobov space in the worst-case setting — a complete picture

Abstract

In this paper, we study tractability of L2-approximation of one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are of product form. For the algorithms we allow information from the class Λall consisting of all continuous linear functionals and from the class Λstd, which only consists of function evaluations. We provide necessary and sufficient conditions on the weights of the function space for quasi-polynomial tractability, uniform weak tractability, weak tractability and (σ,τ)-weak tractability. Together with the already known results for strong polynomial and polynomial tractability, our findings provide a complete picture of the weight conditions for all current standard notions of tractability.