区间上任意连续函数的伯恩斯坦-黎曼内插法公式

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-06-10 DOI:10.1134/S1064562424702028

A. N. Agadzhanov

{"title":"区间上任意连续函数的伯恩斯坦-黎曼内插法公式","authors":"A. N. Agadzhanov","doi":"10.1134/S1064562424702028","DOIUrl":null,"url":null,"abstract":"<p>For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 3","pages":"197 - 205"},"PeriodicalIF":0.5000,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bernstein–Riemann Interpolation Formula for Arbitrary Continuous Functions on an Interval\",\"authors\":\"A. N. Agadzhanov\",\"doi\":\"10.1134/S1064562424702028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.</p>\",\"PeriodicalId\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":\"109 3\",\"pages\":\"197 - 205\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1064562424702028\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702028","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于区间 [0, 1] 上的任意连续函数，我们可以根据这些函数在某个均匀网格上的已知值，得到一个插值公式。无需对函数进行额外假设。这种公式的构造与局部伯恩斯坦多项式和黎曼zeta函数的性质有关。文中给出了黎曼、魏尔斯特拉斯、贝西科维奇和高木类型函数插值的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Bernstein–Riemann Interpolation Formula for Arbitrary Continuous Functions on an Interval

For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.