Reconstruction of high order derivatives by new mollification methods

In this paper,the problem of reconstructing numerical derivatives from noisy data is considered.A new framework of mollification methods based on the L generalized solution regularization methods is proposed.A specific algorithm for the first three derivatives is presented in the paper,in which a modification of TSVD,termed cTSVD is chosen as the regularization technique.Numerical examples given in the paper verify the theoreticai results and show efficiency of the new method.