Abstract: 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 theoretical results and show efficiency of the new method.

Key words: mollification method, L generalized solution, cTSVD method, ill-posed problem, numerical differentiation