GM(1,1)模型的边值分析

Analysis of Boundary Condition for GM(1,1) Model

GM(1,1)模型中边值条件对于生成列微分方程中参数的估计值没有影响 ,但是对于生成序列和原始序列的预测值却有着指数修正效用 .使用均方误差和最小准则 ,针对生成序列和原始序列给出了确定边值修正项的两种方法 .实例表明 。

In GM(1,1) model, the boundary condition has no effect on the identification of parameters in gray differential equation. However, it has an exponential effect on the forecasting value not only for generating but also for original sequences obviously. By minimizing the sum of the squared error, this paper deduces two algorithms of solving boundary value. An example illustrates that it can decrease the forecasting error greatly if we consider the effect of boundary condition.