摘要
讨论了灰色预测GM(1,1)模型理论上存在的一些问题,认为在解微分方程dXdt(1)+aX(1)=b进行预测公式推导时,把-X1(1)=X11作为已知条件来确定微分方程的解是不合理的,而应根据实际情况,不局限于{X(1)(k)}序列,直接从最后的平均相对误差ε-=n1∑k=n1ε(k)入手,将-ε看作是常数cm的函数,求出满足Min{-ε(cm)}的cm值即可,并在此基础上推导出cm的计算公式,形成新的灰色预测公式,从而进一步提高预测精度,最后经过实例验证新的预测公式的正确性及可行性.
This paper discusses some problems of the grey predication model of GM （1,1） exsiting, and points out that in the solution differential equation dX（1）/dt ＋ aX（1）=b,it is unreasonable that X^（1）（1）=X^（1）（1） is looked as the known condition to deduce the predication formula in order to calculate the differential equationrs solution. Instead, according to truth, the known condition should not be limited to the {X^（1）（k）}, and the last average and opposite mistake ^-ε1/n ^n∑k=1｜ε（k）｜ is directly considered, being regarded as the cm′s function. At last, the value of cm is calculated to make the value of ^-ε be the minimum. Based on it, the cm′s formula is conducted, and the new grey prediction formula is formed to improve predication accuracy. Finally, the illustration is used to verify accuracy and feasibility of the predication formula.
出处
《数学的实践与认识》
CSCD
北大核心
2005年第11期11-15,共5页
Mathematics in Practice and Theory
