有限光滑加权Hermite空间中L2逼近和积分的可牵引性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1016/j.jco.2023.101768

Gunther Leobacher , Friedrich Pillichshammer , Adrian Ebert

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引用次数: 0

摘要

在本文中，我们考虑加权Hermite空间中Rs上函数的积分和L2近似。本文的第一部分致力于比较文献中出现的几个加权埃尔米特空间，这本身就很有趣。然后，我们研究了引入Hermite空间的积分和L2近似问题的可处理性，该问题描述了当误差阈值ε趋于0并且问题维数s增长到无穷大时信息复杂度的增长率。我们的主要结果是根据所涉及的权重来刻画可处理性，其对来自加权埃尔米特空间的函数的连续坐标方向的重要性进行了建模。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tractability of L2-approximation and integration in weighted Hermite spaces of finite smoothness

In this paper we consider integration and $L_{2}$ -approximation for functions over $R^{s}$ 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 ε 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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.