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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Reconstruction of high order derivatives from input data

Y. B. Wang / Y. C. Hon / J. Cheng

School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail:

Department of Mathematics, City University of Hong Kong, Hong Kong SAR, China. E-mail:

School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 2, Pages 205–218, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406777571085,

Publication History

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This paper gives a numerical method for reconstructing the original function and its derivatives from discrete input data. It is well known that this problem is ill-posed in the sense of Hadamard. The solution for the first order derivative has been proposed by [10] and [17], using the Tikhonov regularization technique. In this paper, under an assumption that the original function has a square integrable k-th order derivative, we propose a reconstruction method for the j-th order derivative where 0 ≤ jk − 1. A convergence rate estimate is obtained by taking a new choice of the Tikhonov parameter. Numerical example is given to verify the effectiveness and accuracy of the proposed method.

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[2]
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[3]
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[4]
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[6]
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Inverse Problems in Science and Engineering, 2010, Volume 18, Number 7, Page 957
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