A numerical differentiation method and its application to reconstruction of discontinuity
By Yang Wang, X. Jia, Jin Cheng. 2002
119 citations recorded by the source corpus.
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.
Subfields: Biomedical Engineering, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/5c185554e0850bc69df408a083f197e25f19fa24
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Citations in the corpus
- Numerical Differentiation of Approximated Functions with Limited Order-of-Accuracy Deterioration (2012, methodology): “The LDC algorithm presented in this paper offers a number of advantages over those introduced earlier: (1) it is extremely simple—it only requires simple polynomial interpolations and Chebyshev approximations, both of low order; (2) its theoretical analysis leads to an effective strategy for selecti”