| 复有理型插值一致逼近函数及其导数 |
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| 引用本文： | 涂天亮. 复有理型插值一致逼近函数及其导数[J]. 数学杂志, 2006, 26(4): 379-388 |
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| 作者姓名： | 涂天亮 |
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| 作者单位： | 华北水电学院数学与信息系,河南,郑州,450011 |
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| 基金项目： | Supported by NSF of Henan Province P. R. China (974050900) |
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| 摘 要： | 本文研究在单位圆周{|z| =1}上一致逼近函数f(z)及其导数,利用Hermite插值中的基函数建立复有理型插值,并证明它们在{|z| =1}上分别一致收敛于f(z)或f′(z) ,给出了收敛速度.
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| 关 键 词： | 复有理型插值 一致逼近 收敛速度 |
| 文章编号： | 0255-7797（2006）04-0379-10 |
| 收稿时间： | 2004-05-20 |
| 修稿时间： | 2004-05-20 |
COMPLEX RATIONAL TYPE INTERPOLATION UNIFORMLY APPROXIMATES A FUNCTION AND ITS DERIVATIVE |
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| TU Tian-liang. COMPLEX RATIONAL TYPE INTERPOLATION UNIFORMLY APPROXIMATES A FUNCTION AND ITS DERIVATIVE[J]. Journal of Mathematics, 2006, 26(4): 379-388 |
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| Authors: | TU Tian-liang |
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| Affiliation: | Dept. of Math. and Information, North China Institute of Water Conservance and Hydroelectric Power,Zhengzhou 450011, China |
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| Abstract: | In this paper,uniform approximation to a function f(z) and its derivative on unit circle {|z|=1} is researched. Using fundamental functions of Hermite interpolation, we construct the complex rational type interpolations and prove that they uniformly converge to f(z) or f′(z) on {|z|=1} respectively. The rates of convergence are given. |
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| Keywords: | Complex rational type interpolation uniform approximation rate of convergence |
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