{"title":"凸分区上分段常数对两次连续可微函数逼近饱和阶的较低估计","authors":"O. Kozynenko","doi":"10.15421/241805","DOIUrl":null,"url":null,"abstract":"We consider the problem of approximation order of twice continuously differentiable functions of many variables by piecewise constants. We show that the saturation order of piecewise constant approximation in $$$L_p$$$ norm on convex partitions with $$$N$$$ cells is $$$N^{-2/(d+1)}$$$, where $$$d$$$ is the number of variables.","PeriodicalId":339757,"journal":{"name":"Dnipro University Mathematics Bulletin","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Lower estimates on the saturation order of approximation of twice continuously differentiable functions by piecewise constants on convex partitions\",\"authors\":\"O. Kozynenko\",\"doi\":\"10.15421/241805\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of approximation order of twice continuously differentiable functions of many variables by piecewise constants. We show that the saturation order of piecewise constant approximation in $$$L_p$$$ norm on convex partitions with $$$N$$$ cells is $$$N^{-2/(d+1)}$$$, where $$$d$$$ is the number of variables.\",\"PeriodicalId\":339757,\"journal\":{\"name\":\"Dnipro University Mathematics Bulletin\",\"volume\":\"8 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/10.15421/241805\",\"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/10.15421/241805","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lower estimates on the saturation order of approximation of twice continuously differentiable functions by piecewise constants on convex partitions
We consider the problem of approximation order of twice continuously differentiable functions of many variables by piecewise constants. We show that the saturation order of piecewise constant approximation in $$$L_p$$$ norm on convex partitions with $$$N$$$ cells is $$$N^{-2/(d+1)}$$$, where $$$d$$$ is the number of variables.
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