一个基于背景值和初始条件优化的GM(1,1)模型

摘要

背景值和初始条件对GM(1,1)模型的拟合和预测有着极大的影响,通过优化模型的背景值,赋予边值条件为修正形式x (1) (n)+β,利用原始序列新预测值的误差在最小二乘意义下最小准则,从而得到了一个新改进的GM(1,1)优化模型.最后,通过计算实例验证了该优化模型具有极高的预测和模拟精度.%The background value and initial condition have an hugely effect on fitting and prediction of GM (1,1) model.By optimizing to background value of model,letting modified form x(1)(n)+1β be the initial condition, and using of the method of minimum squares to minimize the errors of new forecasting value of original sequence,the new GM (1,1) model are put forward in this paper.At last,the application of computation results show that the optimized new GM (1,1) has a very high fitting and prediction precision.