An optimal GM(1,1) based on the discrete function with exponential law

We prove that accumulated the discrete function with homogeneous exponential law,the discrete function with non-homogeneous exponential law is generated while inversely-accumulated the discrete function with non-homogeneous exponential law,the discrete function with homogeneous exponential law is generated.Based on the error analysis of the GM(1,1) model,we use the discrete function with non-homogeneous exponential law to fit the accumulated sequence to propose a new method to optimize the background value in GM(1,1) model.By contrasting the optimum one to the GM about the simulation,it can be concluded that the new model's fitting precision and prediction precision is improved,and breaks the restricted zone of the developing coefficient.