A stabilized algorithm for multi-dimensional numerical differentiation | Zendy

Zhenyu Zhao | Zendy; Zehong Meng | Zendy; Liang Zhao | Zendy; Lei You | Zendy; Ou Xie | Zendy

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A stabilized algorithm for multi-dimensional numerical differentiation

Author(s) -

Zhenyu Zhao,

Zehong Meng,

Liang Zhao,

Lei You,

Ou Xie

Publication year - 2016

Publication title -

journal of algorithms and computational technology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.234

H-Index - 13

eISSN - 1748-3026

pISSN - 1748-3018

DOI - 10.1177/1748301816640450

Subject(s) - tikhonov regularization , regularization (linguistics) , numerical differentiation , backus–gilbert method , a priori and a posteriori , mathematics , smoothness , regularization perspectives on support vector machines , numerical analysis , algorithm , term (time) , mathematical analysis , mathematical optimization , computer science , inverse problem , artificial intelligence , physics , philosophy , epistemology , quantum mechanics

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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