Numerical weighted integration of functions having mixed smoothness

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1016/j.jco.2023.101757

Dinh Dũng

引用次数: 0

Abstract

We investigate the approximation of weighted integrals over $R^{d}$ for integrands from weighted Sobolev spaces of mixed smoothness. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to n integration nodes for functions from these spaces. In the one-dimensional case $(d = 1)$ , we obtain the right convergence rate of optimal quadratures. For $d \geq 2$ , the upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic crosses in the function domain $R^{d}$ .

查看原文本刊更多论文

混合光滑函数的数值加权积分

我们研究了混合光滑加权Sobolev空间中被积函数在Rd上的加权积分的逼近。对于来自这些空间的函数，我们证明了关于n个积分节点的最优象限的收敛速度的上界和下界。在一维情形（d=1）中，我们获得了最优象限的正确收敛速度。对于d≥2，上界由函数域Rd中阶跃双曲交叉上具有积分节点的稀疏网格象限执行。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.