Bernstein算子和Grünwald算子的线性组合

Bernstein算子和Grünwald算子的线性组合

王淑云¹, 何甲兴¹, 成丽波²

1. 吉林大学数学学院，长春 130012; 2. 长春理工大学基础部，长春 130022

收稿日期:2004-03-02 修回日期:1900-01-01 出版日期:2005-01-26 发布日期:2005-01-20
通讯作者: 王淑云

On Linear Combination of Bernstein and Grünwald Operators

WANG Shu-yun¹, HE Jia-xing¹, CHENG Li-bo²

1. College of Mathematics, Jilin University, Changchun 130012, China;2. Department of Foundation, Changchun University of Science and Technology, Changchun 130022, China

Received:2004-03-02 Revised:1900-01-01 Online:2005-01-26 Published:2005-01-20
Contact: WANG Shu-yun

摘要/Abstract

摘要： 以第一类n阶Chebyshev多项式的零点作为插值节点，通过Bernstein算子和Grünwald算子的线性组合构造一个新算子G_n(f;x). 如果f(x)∈C^j_{［-1,1］_{(0≤j≤9), 则G_n(f;x)在区间

［-1,1］上一致收敛于f(x)∈C^j_［-1,1］(0≤j≤9), 并且其收敛

阶达到最佳, 饱和阶为1/n¹⁰.}}

关键词: Bernstein算子, Grünwald算子, 收敛阶, 饱和阶

Abstract: In this paper a new operator G_n(f;x) is constrcucted by means of the linear combination of Bernstein and Grünwald operators on the basis of taking the zeros of the first kind of Chebyshev polynomial of degreen as the interpolating nodes. G_n(f;x) converges to the f(x)∈C^j_［-1,1］, 0≤j≤9 on ［-1,1］ uniformly and has the best approximation order if the function f(x)∈C^j_［-1,1］, 0≤ j≤9. The saturation order is 1/n¹⁰.

Key words: Bernstein operator, Grünwald operator, convergence order, saturation order

中图分类号:

O174.41

王淑云, 何甲兴, 成丽波. Bernstein算子和Grünwald算子的线性组合[J]. J4, 2005, 43(01): 5-9.

WANG Shu-yun, HE Jia-xing, CHENG Li-bo. On Linear Combination of Bernstein and Grünwald Operators[J]. J4, 2005, 43(01): 5-9.

[1]	刘天宝, 王彩玲, 马明娟, 左平. 一族带有个参数的三阶收敛迭代方法[J]. J4, 2012, 50(4): 711-714.
[2]	刘天宝, 王鹏. 求解非线性方程的一族预估校正迭代方法[J]. J4, 2012, 50(03): 472-.
[3]	刘天宝, 王鹏. 解非线性方程的一族三阶迭代方法[J]. J4, 2012, 50(01): 73-76.
[4]	刘天宝, 吕显瑞. 解非线性方程的一族修正Chebyshev-Halley迭代方法[J]. J4, 2011, 49(06): 1055-1057.
[5]	孙毅, 杨荣, 张旭利. NeumannBessel级数的收敛性[J]. J4, 2008, 46(02): 179-182.
[6]	孟佳娜, 何甲兴. 几个三角求和算子的线性组合[J]. J4, 2005, 43(04): 407-410.
[7]	孙雪楠, 何甲兴, 崔茂源. 一类组合型三角插值多项式[J]. J4, 2004, 42(01): 22-26.
[8]	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.