A note on Lototsky–Bernstein bases

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

引用次数: 0

Abstract

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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关于洛托茨基-伯恩斯坦基的说明

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 $O(n^{-2})$ 。

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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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

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