When GM (1, 1) model is applied to simulate a pure exponential sequence, the errors usually occur. There are many kinds of limitation to the development coefficient and the primary sequence. The characteristics of the discrete GM (1, 1) model are analogous to the GM (1, 1) model. It can be regarded as the precise form of the formal model. The paper studied the growth rate of the simulation values under different initial values of discrete GM (1, 1) model. Applying optimization technique to solve the initial value, it proved that the modified discrete GM(1,1) model can perfectly simulate the exponential sequence.
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