| THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR ｜x｜^α（2〈α〈4）AT EQUIDISTANT NODES |
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| 作者姓名： | Hui Su Shusheng Xu |
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| 作者单位： | East China University of Science and Technology, China |
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| 摘 要： | It is a classical result of Bernstein that the sequence of Lagrange interpolation polumomials to ｜x｜ at equally spaced nodes in -1, 1] diverges everywhere, except at zero and the end-points. In the present paper, toe prove that the sequence of Lagrange interpolation polynomials corresponding to ｜x｜^α （2 〈 α 〈 4） on equidistant nodes in -1, 1] diverges everywhere, except at zero and the end-points.
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| 关 键 词： | 拉格朗日插值 等距节点 散度 多项式 |
| 收稿时间： | 2005-10-31 |
The divergence of Lagrange interpolation for |x|α (2 < α < 4) at equidistant nodes |
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| Hui Su Shusheng Xu.The divergence of Lagrange interpolation for |x|α (2 < α < 4) at equidistant nodes[J].Analysis in Theory and Applications,2006,22(2):146-154. |
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| Authors: | Hui Su Shusheng Xu P R China |
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| Institution: | 1. Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, 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 equally spaced nodes
in −1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange
interpolation polynomials corresponding to |x|α (2 < α < 4) on equidistant nodes in −1, 1] diverges everywhere, except at zero and the end-points. |
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| Keywords: | Lagrange interpolation equidistant nodes divergence |
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