| 关于广义Freud型权的加权Lagrange插值算子的加权Lebesgue数 |
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| 引用本文： | 张珊珊.关于广义Freud型权的加权Lagrange插值算子的加权Lebesgue数[J].兰州大学学报(自然科学版),2007,43(4):110-113,117. |
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| 作者姓名： | 张珊珊 |
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| 作者单位： | 天津师范大学,数学系,天津,300074 |
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| 基金项目： | 国家自然科学基金，天津市教委资助项目 |
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| 摘 要： | 研究以广义Freud型权的正交多项式的零点为插值结点列的加权Lagrange插值算子的加权Lebesgue数的估计问题.证明了以n次正交多项式的零点作为插值结点组的加权Lagrange插值的加权Lebesgue数的阶为n1/6,但以n-2次正交多项式的零点结合两个特别的点作为插值结点组可使得相应的加权Lebesgue数达到最优阶log n.
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| 关 键 词： | 广义Freud型权 加权Lagrange插值 加权Lebesgue数 正交多项式 |
| 文章编号： | 0455-2059（2007）04-0110-05 |
| 修稿时间： | 2005-06-202006-11-01 |
Weighted Lebesgue constant of weighted Lagrange interpolation for generalized Freud-type weights |
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| ZHANG Shan-shan.Weighted Lebesgue constant of weighted Lagrange interpolation for generalized Freud-type weights[J].Journal of Lanzhou University(Natural Science),2007,43(4):110-113,117. |
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| Authors: | ZHANG Shan-shan |
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| Institution: | Department of Mathematics, Tianjin Normal University, Tianjin 300074, China |
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| Abstract: | the weighted Lebesgue constant of weighted Lagrange interpolation is discussed based on the zeros of the orthonormal polynomials with generalized Freud-type weights. The exact order of the corresponding 1 quantity is proved to be n1/6, two proper points can be added to the the zeros such that the exact order of the corresponding quantity is log n. |
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| Keywords: | generalized Freud-type weight weighted Lagrange interpolation weighted Lebesgue constant orthonormal polynomial |
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