Grey GM(1,1,βk) Model and its Application in R&D Personnel

In order to extend the GM(1,1,beta) model, the background value coefficient sequence and the grey differential equation GM(1,1,beta(k)) are defined in this paper. The solution's explicit expression and prediction equation of the grey differential equation GM(1,1,beta(k)) are presented and the iterative algorithms for computing the background value coefficient sequence of the quasi smooth sequence are put forward. Next the GM(1,1,beta(k)) model is applied to forecast China R&D personnel, and compared by several examples. The results show that the grey differential equation GM(1,1,beta(k)) is an identity equation about the background value coefficient in the condition of least residual square sum, the optimization of background value coefficient sequence is related to the relative error of the simulation value, and the optimum solution of the grey differential equation GM(1,1,beta(k)) is equal to that of its whitening differential equation. The examples show that the GM(1,1,beta(k)) model proposed in this paper can not only get better prediction accuracy of the existing method, but also can get higher simulation accuracy.