基于L曲线与de Boor算法的正则化参数选取方法

Regularization Parameters Choosing Method Based on L-curve and de Boor Algorithm

针对数值微分中的参数选取问题,提出一种基于L曲线与de Boor算法的新型正则化参数选取方法:利用基于Hansen的正规化数据包的L曲线对函数进行平滑处理,采用de Boor算法对平滑处理后的函数进一步优化,进而借助正则化方法选择最优参数.为了验证所提方法的有效性,在Matlab中进行了数值仿真.二阶导数近似的仿真结果表明,提出的方法可以实现参数的准确选择,从而大幅度提高了函数逼近的精确性.

A novel regularization parameters choosing method based on L-curve and de Boor algorithm is proposed for numerical differentiation：the L-curve based on regularization package of Hansen is used to smooth the function,and the de Boor algorithm is adopted to optimize the smoothed function,then the regularization method is utilized to choose the optimal parameters.In order to validate the proposed method,some numerical simulations are carried out,and the results on approximation of second-order derivatives show that the proposed method can realize the precise choosing of parameters,which can improve the precision of numerical differentiation substantially.