A numerical differentiation method and its application to reconstruction of discontinuity
A numerical differentiation method and its application to reconstruction of discontinuity
复制标题
DOI：
10.1088/0266-5611/18/6/301
复制
发表时间：
2002-12
期刊：
影响因子：
2.1
通讯作者：
Yang Wang;X. Jia;Jin Cheng
中科院分区：
文献类型：
--
作者：
Yang Wang;X. Jia;Jin Cheng
在本文中，我们讨论了一个经典的不适定问题——吉洪诺夫正则化的数值微分。基于该病态问题的条件稳定性估计，提出了一种选择正则化参数的新简单方法。我们证明，当精确解在 H2 中时，它具有几乎最佳的收敛速度。我们的方法的优点是：（1）与其他方法相比，我们可以用更少的计算量获得相似的计算结果；（2）我们可以在数值上找到不连续点。
In this paper, we discuss a classical ill-posed problem—numerical differentiation by the Tikhonov regularization. Based on the conditional stability estimate for this ill-posed problem, a new simple method for choosing regularization parameters is proposed. We show that it has an almost optimal convergence rate when the exact solution is in H2. The advantages of our method are (1) we can get similar computational results with much less computation, in comparison with other methods, and (2) we can find the discontinuous points numerically.