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

Abstract

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

CLC Number:

O174.4

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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References 26

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

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