A note about exponential tractability of linear weighted tensor product problems in the worst-case setting
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915880761294848 |
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| 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 |
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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 |