【摘要】 针对传统的GM(1,1)灰色预测模型背景值采用均等权值导致预测精度不高的缺点,本文提出一种变权优化选择背景值方法。首先将黄金分割搜索和抛物线插值法相结合确定改进GM(1,1)模型的背景值;然后将改进后的背景值代入灰色预测代数递推方程,从而代替传统的GM(1,1)模型中的白化方程;最后选取指数数列进行模拟并结合某高校教师人数的实际统计数据进行仿真实验。结果表明,改进的GM(1,1)模型减少了平均相对误差,提高了预测精度,具有一定的应用价值。更多还原

【Abstract】 In view of the disadvantage that the traditional GM( 1,1) grey prediction model adopts equal weight in the background value,which results in low prediction accuracy,this paper proposes a variable weight optimization method for selecting background value.Firstly,the golden section search and parabolic interpolation method are combined to determine the background value of the improved GM( 1,1) model.Then the improved background value is brought into the grey prediction algebraic recursive equation,replacing the whitening equation in the traditional GM( 1,1) grey prediction model.Finally,we select the exponential sequence to simulate,and carry out a simulation experiment based on the actual statistical data of the number of teachers in a university.The results show that the improved GM( 1,1) model reduces the average relative error,improves the prediction accuracy and has certain application value.更多还原