第三型伯恩斯坦插值过程的双结点修正

数学季刊 ›› 2008, Vol. 23 ›› Issue (4): 559-564.

第三型伯恩斯坦插值过程的双结点修正

1. Department of Mathematics,Baicheng Teacher's College,Baicheng 137000,China2. Department of Mathematics and Information Science,Yantai University,Yantai 264005,China

收稿日期:2004-09-22 出版日期:2008-12-30 发布日期:2023-09-15
作者简介: CHANG Yu-bao(1970-), male, native of Baicheng, Jilin, a lecturer of Baicheng Teacher's College, M.S.D, engages in function approximation theory.
基金资助:
Supported by the National Natural Science Foundation of China(10626045)；

On Double Revised Nodes of S N Bernstein Interpolation Process of the Third Type

1. Department of Mathematics,Baicheng Teacher's College,Baicheng 137000,China2. Department of Mathematics and Information Science,Yantai University,Yantai 264005,China

Received:2004-09-22 Online:2008-12-30 Published:2023-09-15
About author: CHANG Yu-bao(1970-), male, native of Baicheng, Jilin, a lecturer of Baicheng Teacher's College, M.S.D, engages in function approximation theory.
Supported by:
Supported by the National Natural Science Foundation of China(10626045)；

摘要/Abstract

摘要： In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.

关键词: interpolation polynomial, uniform convergence, the highest convergence order, S N Bernstein problem

Abstract: In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.

Key words: interpolation polynomial, uniform convergence, the highest convergence order, S N Bernstein problem

中图分类号:

O174.41

常玉宝, 魏平, 袁学刚. 第三型伯恩斯坦插值过程的双结点修正[J]. 数学季刊, 2008, 23(4): 559-564.

CHANG Yu-bao, WEI Ping, YUAN Xue-gang. On Double Revised Nodes of S N Bernstein Interpolation Process of the Third Type[J]. Chinese Quarterly Journal of Mathematics, 2008, 23(4): 559-564.

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