| THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES |
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| 引用本文： | LuZhikang XiaMao. THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES[J]. 分析论及其应用, 2003, 19(2): 160-165. DOI: 10.1007/BF02835241 |
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| 作者姓名： | LuZhikang XiaMao |
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| 作者单位： | HangzhouTeacher‘sCollege,China |
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| 摘 要： | It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to [x] at equally spaced nodes in [- 1,1 ] diverges everywhere, except at zero and the end-points. In this paper we show that the sequence of Lagrange interpolation polynomials corresponding to the functions which possess better smoothness on equidistant nodes in [- 1,1 ] still diverges every where in the interval except at zero and the end-points.
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| 关 键 词： | 序列 矩阵 巴拿赫空间 连续 Lagrange插值 节点 散度 |
| 收稿时间： | 2003-06-23 |
The divergence of Lagrange interpolation in equidistant nodes |
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| Lu Zhikang,Xia Mao. The divergence of Lagrange interpolation in equidistant nodes[J]. Analysis in Theory and Applications, 2003, 19(2): 160-165. DOI: 10.1007/BF02835241 |
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| Authors: | Lu Zhikang Xia Mao |
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| Affiliation: | (1) Department of Mathematics, Hangzhou Teacher’s College, 310012 Hangzhou, P. R. China |
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| Abstract: | It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to x at e-qually spaced nodes in [-1.1] diverges everywhere. except at zero and the end-points. In this paper we show that the sequence of Lagrange interpolation polynomials corresponding to the functions which possess better smoothness on equidistant nodes in [-1.1] still diverges every -where in the interval except at zero and the end-points. |
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| Keywords: | lagrange interpolation equidistant nodes divergence |
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