The Applying of Discrete Regularization Method in Numerical Differentiation

Abstract

The numerical differentiation is a typical inverse problem, it is known to be ill-posed in the sense of Hadamard that small perturbations in the function to be differentiated may lead to large errors in the computed derivative. Based on continuous regularization theory, this paper discusses some theoretic and technical problems of applying the discrete regularization method to do the problem of numerical differentiation, among which, the analysis on convergence and stability of discrete regularization solution, the selection of regularization parameter with and without knowing the error level of the input data, the development of the stable algorithms, are concerned and presented, and comparing stability and anti-jamming of the discrete regularization method in this paper and several traditional numerical differentiation methods. and the numerical tests with comparison study are also given based on Matlab.