English

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

Computational Complexity 2026-03-24 v1

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)(s, t)-weak tractability (EXP-(s,t)(s, t)-WT) with max(s,t)<1\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)(s, t)-WT with max(s,t)<1\max(s, t) < 1 and for EXP-UWT.

Keywords

Cite

@article{arxiv.2603.21007,
  title  = {A note about exponential tractability of linear weighted tensor product problems in the worst-case setting},
  author = {Zirong Liu and Heping Wang and Kai Wang},
  journal= {arXiv preprint arXiv:2603.21007},
  year   = {2026}
}

Comments

18 pages

R2 v1 2026-07-01T11:31:49.495Z