An $\ell^1$ Regularized Method for Numerical Differentiation Using Empirical Eigenfunctions
Received:April 25, 2017  Revised:May 25, 2017
Key Word: numerical differentiation   empirical eigenfunctions   $\ell^1$ regularization   mercer kernel  
Fund ProjectL:Supported by the National Nature Science Foundation of China (Grant Nos.11301052; 11301045; 11271060; 11601064; 11671068), the Fundamental Research Funds for the Central Universities (Grant No.DUT16LK33) and the Fundamental Research of Civil Aircraft (Grant No.MJ-F-2012-04).
Author NameAffiliation
Junbin LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Renhong WANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Min XU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      We propose an $\ell^1$ regularized method for numerical differentiation using empirical eigenfunctions. Compared with traditional methods for numerical differentiation, the output of our method can be considered directly as the derivative of the underlying function. Moreover, our method could produce sparse representations with respect to empirical eigenfunctions. Numerical results show that our method is quite effective.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.04.011
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