Numerical Differentiation Algorithm Research And Application

Numerical differentiation is classical ill-posed problem in the sense of Hadamard. The small errors in the measurement may cause significant errors in the numerical results, this problem has been treated by some methods.In this paper, we structure the stable numerical algorithm of known function derivative by using four methods respectively. Firstly,we transform the numerical differentiation problem to the operator equation of the first kind,and then structure the regularization algorithm based on the theory of spectral analysis;how to structure numerical algorithm by using Galerkin and collocation method of projection method;how to structure numerical differentiation algorithm based on discrete singular convolution algorithm by using the nature of delta function;how to structure numerical differentiation algorithm based on the method of dynamic system.Finally,we give theoretical analysis and numerical experiments for every method in this paper.So we can see their advantages and disadvantages.