| 单调序列的非齐次GM(1,1)模型 |
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| 引用本文： | 郭金海,杨锦伟.单调序列的非齐次GM(1,1)模型[J].数学的实践与认识,2014(22). |
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| 作者姓名： | 郭金海 杨锦伟 |
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| 作者单位： | 长江大学信息与数学学院;武汉理工大学理学院;平顶山学院数学与信息科学学院; |
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| 基金项目： | 高等学校博士学科点专项科研基金(20120143110001);教育发展社科基金(11YJC630155);湖北省青年基金(Q20121203);平顶山学院中青年骨干教师培养资助项目(20128024) |
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| 摘 要： | GM(1,1)模型的白化解为齐次指数形式,而一般数据呈非齐次指数形式,存在形式上的差异.本文运用非齐次级比与非齐次指数函数的对应关系,对原始序列中相邻数据做差处理,得到新的序列,将非齐次指数序列转换为齐次指数序列,再建立GM(1,1)模型.实例表明,运用初值优化和非齐次化能提高GM(1,1)模型的精度.
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| 关 键 词： | GM(1 1)模型 平移变换 函数变换 非齐次级比 单调序列 |
Non-homogeneous GM(1,1) Model of Monotonic Sequence |
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| Abstract: | The form of whitening solution of GM(1,1) model is homogeneous exponential,while that of general data is non-homogeneous exponential,there are differences in two forms.In this paper,we firstly apply the corresponding relationship between the non-homogeneous class ratio and non-homogeneous exponential function,and do difference processing to the original sequence adjacent data to get a new sequence,which change the non-homogeneous exponential sequence to a homogeneous one,then establish a GM(1,1) model.The application example shows that the fit precision of the initial value modify model and non-homogeneous grey model can be enhanced. |
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| Keywords: | GM(1 1) model translation transformation function transformation nonhomogeneous class ratio |
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