{"title":"Approximating Reproducing Kernel Hilbert Space Functions by Bernstein Operators","authors":"Han Feng, Sonia Y. W. Hui, Ruohan Shen","doi":"10.1007/s00025-024-02253-w","DOIUrl":null,"url":null,"abstract":"<p>Motivated by kernel methods in machine learning theory, we study the uniform approximation of functions from reproducing kernel Hilbert spaces by Bernstein operators. Rates of approximation are provided in terms of the function norm in the reproducing kernel Hilbert space. A case study of contracting properties of the Bernstein operators is also presented.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00025-024-02253-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Motivated by kernel methods in machine learning theory, we study the uniform approximation of functions from reproducing kernel Hilbert spaces by Bernstein operators. Rates of approximation are provided in terms of the function norm in the reproducing kernel Hilbert space. A case study of contracting properties of the Bernstein operators is also presented.
期刊介绍：
Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.
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