A note about exponential tractability of linear weighted tensor product problems in the worst-case setting
For researchers in information-based complexity, this resolves open questions on exponential tractability of tensor product problems.
The paper fills remaining gaps in exponential tractability for weighted linear tensor product problems, providing necessary and sufficient conditions for EXP-(s,t)-WT with max(s,t)<1 and EXP-UWT in the worst-case setting.
This paper is devoted to discussing the weighted linear tensor product problems in the worst case setting. We consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We investigate exponential $(s, t)$-weak tractability (EXP-$(s, t)$-WT) with $\max(s,t)<1$ and exponential uniform weak tractability (EXP-UWT) under the absolute or normalized error criterion. We solve the problem by filling the remaining gaps left open on EXP-tractability. That is, we obtain necessary and sufficient conditions for EXP-$(s, t)$-WT with $\max(s, t) < 1$ and for EXP-UWT.