The improvement of discrete GM(1,1) prediction model and its solution arithmetic

The GM(1,1) model assume the sequence is analogous to exponential law. Great error appears when it is used to simulate many nonlinear sequences. The paper proves that the growth rates of the simulated value of the GM(1,1) model and the discrete GM(1,1) model are both fixed value. If the growth rates of the primary sequence are equate, the fitted value deriving from the discrete GM(1,1) model the same as the primary sequence. The paper improves the discrete GM(1,1) model. Using the optimization method, the paper studies the initial value. The paper puts forward the solution arithmetic to the optimization and proves the efficiency of the arithmetic by means of a example. The research indicates the discrete grey extension model can greatly improve the simulated intensity and it can solve the simulated of the nonlinear nonnegative sequence.