{"title":"利用盒形分区上的调和样条,研究了有界拉普拉斯函数的最佳超限插值的阶数","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":"{\"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}","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}
The order of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions
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 $$$N \rightarrow \infty$$$.