Reconstruction of high order derivatives from input data
Reconstruction of high order derivatives from input data
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DOI：
10.1515/156939406777571085
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发表时间：
2006-04
期刊：
影响因子：
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通讯作者：
Y. B. Wang;Y. Hon;Jin Cheng
中科院分区：
文献类型：
--
作者：
Y. B. Wang;Y. Hon;Jin Cheng
本文给出了一种从离散输入数据重建原始函数及其导数的数值方法。众所周知，这个问题在Hadamard意义下是不适定的。一阶导数的解已由[10]和[17]利用Tikhonov正则化技术提出。本文在原函数具有平方可积k阶导数的假设下，提出了一种重构j阶导数的方法，其中0≤j≤k−1.通过重新选择Tikhonov参数，得到了收敛速度估计.数值算例验证了该方法的有效性和准确性。
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.