| 一类新型求和算子的最佳一致逼近 |
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| 引用本文： | 孟佳娜,周学勤.一类新型求和算子的最佳一致逼近[J].烟台大学学报(自然科学与工程版),2006,19(2):83-87,124. |
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| 作者姓名： | 孟佳娜 周学勤 |
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| 作者单位： | 1. 烟台大学,计算机学院,山东,烟台,264005
2. 烟台大学,数学与信息科学系,山东,烟台,264005 |
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| 基金项目： | 中国科学院资助项目;烟台大学校科研和教改项目 |
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| 摘 要： | 鉴于Lagrange插值多项式算子并非对任意的连续函数都能够一致收敛，为改善其收敛性，构造了一类基于等距结点组下的新型三角多项式求和算子．不仅证明了新算子在整个实轴上一致收敛于任意以2π为周期的连续函数，同时还得到了算子的最佳逼近阶．与其他三角求和算子相比，新算子的收敛性要明显优于其他算子．特别地，新算子的最高逼近阶明显高于目前已有的求和算子．
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| 关 键 词： | 三角求和算子 线性组合 一致收敛 最佳逼近阶 |
| 文章编号： | 1004-8820（2006）02-0083-05 |
| 收稿时间： | 2005-06-11 |
| 修稿时间： | 2005-06-11 |
On the Best Uniform Approximation of a New Class of Summation Operators |
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| MENG Jia-na,ZHOU Xue-qin.On the Best Uniform Approximation of a New Class of Summation Operators[J].Journal of Yantai University(Natural Science and Engineering edirion),2006,19(2):83-87,124. |
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| Authors: | MENG Jia-na ZHOU Xue-qin |
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| Institution: | 1. School of Computer, Yantai University, Yantai 264005, China; 2. Department of Mathematics and Informational Science, Yantai University, Yantai 264005, China |
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| Abstract: | Due to the functions uniformly, we Lagrange interpolation construct a new class of operators do not converge to arbitrary continuous triangle summation operators based on the equidistant nodes to improve its convergence property. We not only prove that the new operator converges to arbitrary continuous functions with period 2w uniformly on the whole axis, but also obtain the best approximation order simultaneously. In contrast to other triangle summation operators, the convergence properties of the new operator is superior to others. In particular, the highest approximation order is higher than other obtained summation operators. |
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| Keywords: | triangle summation operator linear combination uniform convergence the best approximation order |
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