加权 Korobov 空间中多元 $\mathbb{L}_{\infty}$-逼近问题的指数收敛易处理性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 525-538.

加权 Korobov 空间中多元 $\mathbb{L}_{\infty}$-逼近问题的指数收敛易处理性

张杰^1,^*(),孙艺铭¹(),刘永平²()

1.山东建筑大学理学院济南 250101
2.北京师范大学数学科学学院北京 100875

收稿日期:2023-07-31 修回日期:2023-10-17 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *张杰, Email:zhangjie1991@sdjzu.edu.com
作者简介:孙艺铭: Email:sunyimingzz123@163.com;|刘永平: Email:ypliu@bnu.edu.cn
基金资助:
国家自然科学基金(12101369);国家自然科学基金(11871006);山东省高等学校青创团队计划(2022KJ209);山东建筑大学博士基金项目(X19090Z)

EC-tractability of Multivariate $\mathbb{L}_{\infty}$-approximation in Weighted Korobov Spaces

Zhang Jie^1,^*(),Sun Yiming¹(),Liu Yongping²()

1. College of Science, Shandong Jianzhu University, Jinan 250101
2. Department of Mathematics, Beijing Normal University, Beijing 100875

Received:2023-07-31 Revised:2023-10-17 Online:2024-06-26 Published:2024-05-17
Supported by:
NSFC(12101369);NSFC(11871006);Development Plan of Youth Innovation Team of Shandong Provincial Colleges and Universities(2022KJ209);Doctoral Foundation Project of Shandong Jianzhu University(X19090Z)

摘要/Abstract

摘要：

该文主要研究最坏框架下加权 Korobov 空间中多元 $\mathbb{L}_{\infty}$-逼近问题的指数易处理性.多元逼近问题中的算法使用的信息取自由线性泛函组成的线性信息类 $\Lambda^{\text{all}}$和函数值组成的标准信息类 $\Lambda^{\text{std}}$.该问题的指数收敛-拟多项式易处理性和指数收敛-一致弱易处理性之前并没有被研究,该文最终通过两个权参数序列给出使得多元 $\mathbb{L}_{\infty}$-逼近问题具有这两种指数收敛易处理性的充分必要条件.

关键词: 指数收敛易处理性, Korobov 空间, 最坏框架, 多元 $\mathbb{L}_{\infty}$-逼近问题

Abstract:

In this paper we study exponential tractability of multivariate $\mathbb{L}_{\infty}$-approximation for weighted Korobov spaces in the worst case setting. We consider all algorithms that use the class $\Lambda^{\text{all}}$ of all linear functionals and the class $\Lambda^{\text{std}}$ of only function evaluations as information. We give matching necessary and sufficient conditions for notions of EC-quasi-polynomial tractability and EC-uniform weak tractability which have not been discussed before in terms of two weight parameters of the problem.

Key words: Exponential convergence tractability, Korobov spaces, Worst case setting, Multivariate $\mathbb{L}_{\infty}$ -approximation

中图分类号:

O174.4

张杰, 孙艺铭, 刘永平. 加权 Korobov 空间中多元 $\mathbb{L}_{\infty}$-逼近问题的指数收敛易处理性[J]. 数学物理学报, 2024, 44(3): 525-538.

Zhang Jie, Sun Yiming, Liu Yongping. EC-tractability of Multivariate $\mathbb{L}_{\infty}$-approximation in Weighted Korobov Spaces[J]. Acta mathematica scientia,Series A, 2024, 44(3): 525-538.

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