An l^(1) Regularized Method for Numerical Differentiation Using Empirical Eigenfunctions  

作　　者：Junbin LI Renhong WANG Min XU 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology

出　　处：《Journal of Mathematical Research with Applications》2017年第4期496-504,共9页数学研究及应用（英文版）

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)

摘　　要：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.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.

关 键 词：numerical differentiation empirical eigenfunctions ?~1 regularization mercer kernel 

分 类 号：O241.4[理学—计算数学]