About a dubious proof of a correct result about closed Newton Cotes error formulas

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
David J. López, Jose A. Padilla, Juan Ruiz, Carlos Tapia, Juan C. Trillo
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引用次数: 0

Abstract

In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [ a , b ] . \left[a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel.
关于一个关于封闭牛顿柯特误差公式的正确结果的可疑证明
在本研究中,我们评论了闭区间积分的闭牛顿柯特误差公式的一个错误证明,至少是不完整的证明[a, b]。\ [a, b]。这些误差公式是对梯形定则误差公式的简单证明的一种直观的推广,它们的证明有一个有争议的步骤,它把证明变成了恶作剧,或者至少,这一步需要明确说明,它不容易推导。这些公式的正确证明来自一种基于Peano内核的技术。
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来源期刊
Accounts of Chemical Research
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.
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