| THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES |
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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： | 23 June 2003 |
The divergence of Lagrange interpolation in equidistant nodes |
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| LuZhikang XiaMao.THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES[J].Analysis in Theory and Applications,2003,19(2):160-165. |
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| Authors: | Lu Zhikang Xia Mao |
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| Institution: | (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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