{"title":"A note on generalized Floater–Hormann interpolation at arbitrary distributions of nodes","authors":"Woula Themistoclakis, Marc Van Barel","doi":"10.1007/s11075-024-01933-6","DOIUrl":null,"url":null,"abstract":"<p>The paper is concerned with a generalization of Floater–Hormann (briefly FH) rational interpolation recently introduced by the authors. Compared with the original FH interpolants, the generalized ones depend on an additional integer parameter <span>\\(\\gamma >1\\)</span>, that, in the limit case <span>\\(\\gamma =1\\)</span> returns the classical FH definition. Here we focus on the general case of an arbitrary distribution of nodes and, for any <span>\\(\\gamma >1\\)</span>, we estimate the sup norm of the error in terms of the maximum (<i>h</i>) and minimum (<span>\\(h^*\\)</span>) distance between two consecutive nodes. In the special case of equidistant (<span>\\(h=h^*\\)</span>) or quasi–equidistant (<span>\\(h\\approx h^*\\)</span>) nodes, the new estimate improves previous results requiring some theoretical restrictions on <span>\\(\\gamma \\)</span> which are not needed as shown by the numerical tests carried out to validate the theory.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01933-6","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is concerned with a generalization of Floater–Hormann (briefly FH) rational interpolation recently introduced by the authors. Compared with the original FH interpolants, the generalized ones depend on an additional integer parameter \(\gamma >1\), that, in the limit case \(\gamma =1\) returns the classical FH definition. Here we focus on the general case of an arbitrary distribution of nodes and, for any \(\gamma >1\), we estimate the sup norm of the error in terms of the maximum (h) and minimum (\(h^*\)) distance between two consecutive nodes. In the special case of equidistant (\(h=h^*\)) or quasi–equidistant (\(h\approx h^*\)) nodes, the new estimate improves previous results requiring some theoretical restrictions on \(\gamma \) which are not needed as shown by the numerical tests carried out to validate the theory.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
