关于洛托茨基-伯恩斯坦基的说明

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-06 DOI:10.1186/s13660-024-03076-7

Xiao-Wei Xu, Xin Yu, Jia-Lin Cui, Qing-Bo Cai, Wen-Tao Cheng

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引用次数: 0

摘要

在本论文中，我们将研究一类特殊 Lototsky-Bernstein 基的近似性质。我们的重点是通过由 Lototsky-Bernstein 基上的定点生成的近似过程来近似 $[-1,1]$[-1,1]$ 上的 $|x|$。我们的第一个结果表明，$p_{n}(x)$ 对 $|x|$ 的逼近过程保留了 $[-1,1]$ 上的良好形状。此外，我们还得出了一些收敛结果和不等式。我们的第二个主要结果表明，近似的收敛速率为 $O(n^{-2})$ 。

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A note on Lototsky–Bernstein bases

In this note, we study some approximation properties on a class of special Lototsky–Bernstein bases. We focus on approximation of $|x|$ on $[-1,1]$ by an approximation process generated from fixed points on Lototsky–Bernstein bases. Our first result shows that the approximation procedure $p_{n}(x)$ to $|x|$ preserves good shapes on $[-1,1]$ . Moreover, some convergence results and inequalities are derived. Our second main result states that the rate convergence of the approximation is $O(n^{-2})$ .

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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.