Abstract: Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper. In the first place, several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor’s formula. And then, based on the ideas of algebraic accuracy, several inverse problems of numerical differentiation formulae are given.

Key words: numerical differentiation, remainder term, asymptotic property, intermediate point, algebraic precision, inverse problem