第三型伯恩斯坦插值过程的新研究

第三型伯恩斯坦插值过程的新研究

孟佳娜

烟台大学计算机科学与技术学院，烟台 264005

收稿日期:2002-09-13 修回日期:1900-01-01 出版日期:2003-04-26 发布日期:2003-04-26
通讯作者: 孟佳娜

New Studies About the Third Type InterpolationProcess of Bernstein

MENG Jiana

School of Computer Science and Technology, Yantai University, Yantai 264005, China

Received:2002-09-13 Revised:1900-01-01 Online:2003-04-26 Published:2003-04-26
Contact: MENG Jiana

摘要/Abstract

摘要： 对第三型伯恩斯坦插值过程做进一步研究，利用两点修正方法，构造一个算子G_n(f;r,x)，它对于有直到r阶连续导数的f(x)∈C ^jj_［-1,1］(0≤j≤r)都一致收敛，并且得到算子G_n (f;r,x)的最佳收敛阶.

关键词: 第三型伯恩斯坦插值过程, 两点修正, 一致收敛, 最佳收敛阶

Abstract: The present paper deals with the third type interpola tion process of Bernstein in a deep step. An operator G_n(f;r,x) is co nstructed by means of the modified method of two zero nodes. It is proved that the operator converges to arbitrary continuous derivative function f(x)∈C ^j_［-1,1］(0≤j≤r) uniformly and the convergence order of the operator G_n(f;r,x) is the best.

Key words: the third type interpolation process of Bernstein, two zero nodes revision, convergence uniformly, optimal convergence order

中图分类号:

O174.41

孟佳娜. 第三型伯恩斯坦插值过程的新研究[J]. J4, 2003, 41(02): 140-143.

MENG Jiana. New Studies About the Third Type InterpolationProcess of Bernstein[J]. J4, 2003, 41(02): 140-143.

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