Direct modeling approach of DGM(1,1) with approximate non-homogeneous exponential sequence

This paper optimized the initial condition of DGM(1,1) model,and discussed and proved the consistency of the novel model and the original data in the aspects of geometric shape with up,down, concave,convex and etc.Ultimately,some examples show the practicability and validity of the novel modeling approach.The new model has a vital significance for enriching and perfecting the theory system of grey prediction model.