We propose an ？~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 ...We propose an ？~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.展开更多
基金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)the Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)
文摘We propose an ？~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.
