论文标题
部分可观测时空混沌系统的无模型预测
Tractability of $L_2$-approximation and integration in weighted Hermite spaces of finite smoothness
论文作者
论文摘要
在本文中，我们考虑了从加权Hermite空间的$ \ rr^s $上的功能的集成和$ L_2 $ - APPRXIMATION。该论文的第一部分致力于比较文学中出现的几个加权的强力空间，这本身很有趣。然后，我们研究了集成的障碍性和$ L_2 $ - APPRXIMATION问题，用于引入的Hermite空间，该空间描述了当误差阈值$ \ VAREPSILON $趋向于0时，该信息复杂性的增长率且问题尺寸$ s $生长到Infinity。我们的主要结果是根据所涉及的权重来表征障碍性，这模拟了连续的坐标方向从加权的HERMITE空间中的功能的重要性。
In this paper we consider integration and $L_2$-approximation for functions over $\RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature, which is interesting on its own. Then we study tractability of the integration and $L_2$-approximation problem for the introduced Hermite spaces, which describes the growth rate of the information complexity when the error threshold $\varepsilon$ tends to 0 and the problem dimension $s$ grows to infinity. Our main results are characterizations of tractability in terms of the involved weights, which model the importance of the successive coordinate directions for functions from the weighted Hermite spaces.
