The Optimization of the Parameters and the Application of GM (1,1) Model

The first order regression coefficient beta₁ of the discrete GM (1,1) model x⁽¹⁾(k+1)=beta₁x⁽¹⁾(k)+beta₂ is obtained by the method of least squares, then the development coefficient -a is obtained by a=-lnbeta₁, finally b is obtained when the square sum of the difference of the predictive value of x⁽¹⁾(k+1) and x⁽¹⁾(k+1) is the smallest, thus the optimum parameters a and b are got. This paper strictly proves the optimum model has the white exponential law of coincidence. The examples are used to show that the optimum model has the better simulation results and the better prediction results.