优化背景值和时间响应函数的一类直接模型法  

A direct model method based on optimized background value and time response function

作　　者：王健[1] 

机构地区：[1]安阳师范学院数学与统计学院,河南安阳455002

出　　处：《兰州理工大学学报》2017年第2期159-162,共4页Journal of Lanzhou University of Technology

基　　金：河南省高等学校重点科研项目(16B110001)

摘　　要：根据灰色GM(1,1)直接模型原始数据具有非齐次灰指数规律特点,构建出相应的拟合函数,再利用辛普森公式优化模型背景值,同时利用最小二乘法确定时间响应函数中的常数c,得到一种改进的GM(1,1)直接模型.实例分析表明:该改进模型的模拟和预测精度较高,也拓宽了灰色预测模型的使用范围.According to the feature that the original data in the grey GM（1,1） direct model have non- homogeneous pattern, a corresponding fitting function is constructed, the Simpson formula is used to opti- mize the background value of the model and, meantime, the least square method is employed to determine the constant c in time response function, so that an improved GM（1,1） direct model is obtained. The re- sult of analysis of actual example shows that this improved model will have a higher accuracy of simulation and prediction, and extend the application scope of the grey prediction model.

关 键 词：直接模型 背景值 辛普森公式 时间响应函数 预测 

分 类 号：O29[理学—应用数学]