| 基于正交多项式下的数值微分任意阶稳定逼近 |
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| 引用本文： | 吴传生,周洋,黄小为.基于正交多项式下的数值微分任意阶稳定逼近[J].数学杂志,2015,35(2):397-406. |
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| 作者姓名： | 吴传生 周洋 黄小为 |
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| 作者单位： | 武汉理工大学理学院 |
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| 基金项目： | 国家自然科学基金项目(61070009) |
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| 摘 要： | 本文研究了数值微分问题.利用基于正交多项式理论下的积分算子方法,获得了可以稳定逼近已知函数任意阶导数的结果,推广了Lanczos积分方法的结果.
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| 关 键 词： | 数值微分 反问题与不适定问题 正交多项式 积分法 |
| 收稿时间： | 2014/4/2 0:00:00 |
| 修稿时间： | 2014/7/31 0:00:00 |
NUMERICAL DIFFERENTIAL FOR ARBITRARY ORDER APPROXIMATION STEADILY BASED ON ORTHOGONAL POLYNOMIAL |
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| WU Chuan-sheng,ZHOU Yang and HUANG Xiao-wei.NUMERICAL DIFFERENTIAL FOR ARBITRARY ORDER APPROXIMATION STEADILY BASED ON ORTHOGONAL POLYNOMIAL[J].Journal of Mathematics,2015,35(2):397-406. |
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| Authors: | WU Chuan-sheng ZHOU Yang and HUANG Xiao-wei |
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| Institution: | WU Chuan-sheng;ZHOU Yang;HUANG Xiao-wei;School of Sciences,Wuhan University of Technology; |
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| Abstract: | In this paper, we investigate the numerical differentiation of higher order. Based on orthogonal polynomial theory, integral operator method is utilized. Using the proposed method we can estimate any order derivatives of approximately specified functions. The new method also generalized the result of the Lanczos''s. |
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| Keywords: | numerical differentiation ill-posed problem orthogonal polynomial integral method |
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