{"title":"The order of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions","authors":"D. Skorokhodov","doi":"10.15421/241811","DOIUrl":null,"url":null,"abstract":"We show that the error of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions comprising $$$N$$$ elements has the order $$$N^{-2}$$$ as $$$N \\rightarrow \\infty$$$.","PeriodicalId":339757,"journal":{"name":"Dnipro University Mathematics Bulletin","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dnipro University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/241811","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We show that the error of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions comprising $$$N$$$ elements has the order $$$N^{-2}$$$ as $$$N \rightarrow \infty$$$.
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