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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 ≤ 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.
Published Online: --
Published in Print: 2006-04-01
Copyright 2006, Walter de Gruyter
