| An $\ell^1$ Regularized Method for Numerical Differentiation Using Empirical Eigenfunctions |
| Received:April 25, 2017 Revised:May 25, 2017 |
| Key Words:
numerical differentiation empirical eigenfunctions $\ell^1$ regularization mercer kernel
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| Fund Project: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). |
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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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