GM(1,1)模型背景值构造中参数n的公式推导及其应用

摘要

The former could produce a satisfactory result yet the computation is too complicated,while the latter is simple to compute yet is blamed for the lack of a theoretic basis,thus efforts are made to put forth a simple,yet strictly and theoretically based approach to determine the parameter in the background value.The dependence formula of the score n in optimized background value z(1)n (k)and development coefficient a was derived from the strict index sequential form.For the general sequence,the estimation formula of development coefficient is given too.Then based on the dependence formula n is determined,and the optimized background value z(1)n (k)is introduced into gray differential equations to solve the development coefficient a ,thus a prediction model with a nice sphere of application and high simulation accuracy is gained.And case-based examples show that the said method is of high feasibility and superiority.%提出了一个计算简便,而且是经过严格理论推导得出背景值中参数的确定方法。先对严格指数序列形式推导得到优化背景值z(1)n (k)中等分数n与发展系数a 的依赖关系公式,然后对一般序列给出了发展系数的估计式,再根据依赖关系公式求n,最后将优化背景值z(1)n (k)代入灰色微分方程求解发展系数a,进而获得了一个适用范围宽,模拟精度高的预测模型。最后通过实例说明了该方法具有可行性和优越性。