Tractability of approximation in the weighted Korobov space in the worst-case setting -- a complete picture
Adrian Ebert, Friedrich Pillichshammer

TL;DR
This paper provides a comprehensive analysis of the conditions under which $L_2$-approximation in weighted Korobov spaces is tractable, covering all major notions of tractability in the worst-case setting.
Contribution
It offers necessary and sufficient conditions on weights for various tractability notions, completing the understanding of approximation complexity in this setting.
Findings
Characterizes weight conditions for quasi-polynomial tractability
Identifies conditions for uniform and weak tractability
Completes the picture with known results on polynomial tractability
Abstract
In this paper, we study tractability of -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 consisting of all continuous linear functionals and from the class , 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 -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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
