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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 14, Issue 2 (Apr 2006)


Reconstruction of high order derivatives from input data

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

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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Published in Print: 2006-04-01

Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939406777571085.

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