The Optimization of Background Value in GM(1,1) Model

In this paper, we prove that discrete function with non-homogeneous exponential law is generated by accumulating the discrete function with homogeneous exponential law while discrete function with homogeneous exponential law is generated by inversely-accumulating the discrete function with non-homogeneous exponential law. Based on the error analysis of the Model GM(1,1), we use the discrete function with non-homogeneous exponential law to fit the accumulated sequence in order to propose a new method for optimizing background value in Model GM(1,1). By contrasting the optimum model to the GM one with the simulation, it can be concluded that the new model broke through the restricts of adaption coefficient and it still improved its matching and prediction precision.