Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
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Source Normalized Impact per Paper (SNIP) 2015: 1.106
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Reconstruction of high order derivatives from input data
∗School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail: (email)
†Department of Mathematics, City University of Hong Kong, Hong Kong SAR, China. E-mail: (email)
‡School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail: (email)
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,
- Published Online:
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  and , 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 ≤ j ≤ k − 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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