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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Liu, Zirong, Wang, Heping, Wang, Kai
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915880761294848
author Liu, Zirong
Wang, Heping
Wang, Kai
author_facet Liu, Zirong
Wang, Heping
Wang, Kai
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_21007
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note about exponential tractability of linear weighted tensor product problems in the worst-case setting
Liu, Zirong
Wang, Heping
Wang, Kai
Computational Complexity
65Y20, 41A63
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.
title A note about exponential tractability of linear weighted tensor product problems in the worst-case setting
topic Computational Complexity
65Y20, 41A63
url https://arxiv.org/abs/2603.21007