论文标题
在最差的情况下，加权的Korobov空间中近似的障碍性
Tractability of approximation in the weighted Korobov space in the worst-case setting
论文作者
论文摘要
在本文中，我们考虑了来自加权Korobov空间的定期功能，考虑$ l_p $ -approximation，$ p \ in \ {2，\ infty \} $。特别是，我们讨论了此类问题的障碍性能，这意味着我们旨在将信息复杂性对错误需求$ \ varepsilon $和尺寸$ d $与权重序列$（γ_j）_ {j \ ge 1} $分配给Korobob Space的衰减率的依赖性。自从本千年开始以来，一些结果就众所周知，而另一些结果已得到证明。我们对这些发现进行了调查，并将在$ L_ \ infty $ -Approximation问题上添加一些新结果。总而言之，我们简要概述结果并收集许多有趣的开放问题。
In this paper we consider $L_p$-approximation, $p \in \{2,\infty\}$, of periodic functions from weighted Korobov spaces. In particular, we discuss tractability properties of such problems, which means that we aim to relate the dependence of the information complexity on the error demand $\varepsilon$ and the dimension $d$ to the decay rate of the weight sequence $(γ_j)_{j \ge 1}$ assigned to the Korobov space. Some results have been well known since the beginning of this millennium, others have been proven quite recently. We give a survey of these findings and will add some new results on the $L_\infty$-approximation problem. To conclude, we give a concise overview of results and collect a number of interesting open problems.
