关于一个Bernstein型插值过程收敛阶的点态估计

吉林大学学报(工学版) ›› 2001, Vol. ›› Issue (1): 43-46.

关于一个Bernstein型插值过程收敛阶的点态估计

王淑云, 孙毅, 何甲兴

吉林大学南岭校区理学院, 吉林长春 130025

收稿日期:2000-06-03 出版日期:2001-01-25

Study on Estimation of Convergence Order of a New Bernstein Interpolation Process

WANG Shu-yun, SUN Yi, HE Jia-xing

College of Sciences, Jilin University, Nanling Campus, Changchun 130025, China

Received:2000-06-03 Online:2001-01-25

摘要/Abstract

摘要： 主要研究了一个Bernstein型插值多项式H_n(f;x)对C_[-1,1]^j(j=0或 1)连续函数类的逼近阶,改进了文献[1]的结果,即在连续状态下得出点态的逼近阶。

关键词: Bernstein型插值多项式, 逼近阶, 最佳逼近阶

Abstract: In this paper,the authors study the convergence order of the interpolation process of Bernstein polynomial H_n(f;x) approximate to f(x)∈C_[-1,1]^j(j=0 or j=1) on [-1,1].The result of the paper [1] is improved.

Key words: Bernstein interpolation polynomial, convergence order, best aproximation order

中图分类号:

O174.41

王淑云, 孙毅, 何甲兴. 关于一个Bernstein型插值过程收敛阶的点态估计[J]. 吉林大学学报(工学版), 2001, (1): 43-46.

WANG Shu-yun, SUN Yi, HE Jia-xing. Study on Estimation of Convergence Order of a New Bernstein Interpolation Process[J]. 吉林大学学报(工学版), 2001, (1): 43-46.

参考文献

[1] He Jiaxing, Zhang Yulei, Li Songtao. On a new interpolation process of S. N. Bernstein［J］. Acta Math Hungarica, 1996,73(4):327334.
[2] 袁学刚.关于一个Bernstein插值过程收敛阶的新估计［J］.吉林工业大学学报,1997,27(4):59～64.
[3] Varma A K. A new proof of Timan's A. F. approximation theorem［J］. Journal of Approximation Theory, 1976,18:57～62.

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