{"title":"马斯登型缺四次样条的最优性质","authors":"A. Bica, Diana Curilă-Popescu, M. Curila","doi":"10.33993/jnaat492-1228","DOIUrl":null,"url":null,"abstract":"In this work, we obtain an improved error estimate in the interpolation with the Hermite \\(C^{2}\\)-smooth deficient complete quartic spline that has the distribution of nodes following the Marsden type scheme and investigate the possibilities to compute the derivatives on the knots such that the obtained spline \\(S\\in C^{1}[a,b]\\) has minimal curvature and minimal \\(L^{2}\\)-norm of \\(S^{\\prime }\\) and \\(S^{\\prime \\prime \\prime }\\). In each case, the interpolation error estimate is performed in terms of the modulus of continuity.%MCEPASTEBIN%","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Optimal properties for deficient quartic splines of Marsden type\",\"authors\":\"A. Bica, Diana Curilă-Popescu, M. Curila\",\"doi\":\"10.33993/jnaat492-1228\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we obtain an improved error estimate in the interpolation with the Hermite \\\\(C^{2}\\\\)-smooth deficient complete quartic spline that has the distribution of nodes following the Marsden type scheme and investigate the possibilities to compute the derivatives on the knots such that the obtained spline \\\\(S\\\\in C^{1}[a,b]\\\\) has minimal curvature and minimal \\\\(L^{2}\\\\)-norm of \\\\(S^{\\\\prime }\\\\) and \\\\(S^{\\\\prime \\\\prime \\\\prime }\\\\). In each case, the interpolation error estimate is performed in terms of the modulus of continuity.%MCEPASTEBIN%\",\"PeriodicalId\":287022,\"journal\":{\"name\":\"Journal of Numerical Analysis and Approximation Theory\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical Analysis and Approximation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33993/jnaat492-1228\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical Analysis and Approximation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33993/jnaat492-1228","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal properties for deficient quartic splines of Marsden type
In this work, we obtain an improved error estimate in the interpolation with the Hermite \(C^{2}\)-smooth deficient complete quartic spline that has the distribution of nodes following the Marsden type scheme and investigate the possibilities to compute the derivatives on the knots such that the obtained spline \(S\in C^{1}[a,b]\) has minimal curvature and minimal \(L^{2}\)-norm of \(S^{\prime }\) and \(S^{\prime \prime \prime }\). In each case, the interpolation error estimate is performed in terms of the modulus of continuity.%MCEPASTEBIN%
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
