几个三角求和算子的线性组合

几个三角求和算子的线性组合

孟佳娜¹, 何甲兴²

1. 烟台大学计算机学院, 山东省烟台 264005; 2. 吉林大学数学研究所, 长春 130012

收稿日期:2004-09-23 修回日期:1900-01-01 出版日期:2005-07-26
通讯作者: 孟佳娜

Linear Combination of Several Operators of Triangle Summation

MENG Jia-na¹, HE Jia-xing²

1. School of Computer Science and Technology, Yantai University, Yantai 264005, Shandong Province, China; 2. Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2004-09-23 Revised:1900-01-01 Online:2005-07-26
Contact: MENG Jia-na

摘要/Abstract

摘要： 通过对已有几个三角求和算子进行线性组合, 构造一个新算子T_n(f;x). 证明该算子在全实轴上一致收敛于任意以2π为周期的连续函数f(x), 得到了当f(x)∈C^j_2π(0≤j≤7)时算子的最佳收敛阶, 并且证明了算子的最高收敛阶不会超过1/n⁸. 在收敛性方面, 所构造的新算子明显优于其他算子.

关键词: 三角求和算子, 一致收敛, 最佳收敛阶

Abstract: A new triangle summation operator, T_n(f;x), is constructed via linearly combini ng several known operators. It is proved that this operator converges t o arbitrary continuous function f(x) with period 2π on the whole axis. If f(x)∈C^j_2π(0≤j≤7), the best convergence order of the op erator is obtained. Finally, it is proved that the highest convergence order of the operator does not exceed 1/n⁸. The new operator constructed in th is paper is superior to other operators in convergency.

Key words: triangle summation operator, uniform convergence, b est approximation order

中图分类号:

O174.41

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.

MENG Jia-na, HE Jia-xing. Linear Combination of Several Operators of Triangle Summation[J]. J4, 2005, 43(04): 407-410.

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