A stabilized algorithm for multi-dimensional numerical differentiation

被引：8
|
作者：
Zhao, Zhenyu [1 ]
Meng, Zehong [2 ]
Zhao, Liang [3 ]
You, Lei [1 ]
Xie, Ou [1 ]
机构：
[1] Guangdong Ocean Univ, Coll Sci, Zhanjiang 524088, Peoples R China
[2] Zhejiang Univ Finance & Econ, Sch Math & Stat, Hangzhou, Zhejiang, Peoples R China
[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing, Peoples R China
来源：
JOURNAL OF ALGORITHMS & COMPUTATIONAL TECHNOLOGY | 2016年 / 10卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Numerical differentiation; ill-posed problem; Tikhonov regularization method; Hilbert scales;
D O I：
10.1177/1748301816640450
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We develop a multi-dimensional numerical differentiation method in this paper. To obtain stable numerical derivatives, the Tikhonov regularization method in Hilbert scales is proposed to deal with illposedness of the problem. The penalty term in Tikhonov functional is more general so that we can choose the regularization parameter without the smoothness parameter and the a priori bound of exact solution. Numerical examples are also presented to check the effectiveness of the method.
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页码：73 / 81
页数：9
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