A note about exponential tractability of linear weighted tensor product problems in the worst-case setting

Abstract

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.