| 非等间距NGM(1,1,k)模型及其应用 |
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| 引用本文： | 李亚男,曾亮. 非等间距NGM(1,1,k)模型及其应用[J]. 数学的实践与认识, 2017, 0(9): 159-165 |
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| 作者姓名： | 李亚男 曾亮 |
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| 作者单位： | 广东理工学院基础教学部,广东肇庆,526100 |
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| 基金项目： | 广东省高等学校“千百十人才培养工程”第八批校级培养基金，广东理工学院科技项目(GKJ2016002) |
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| 摘 要： | 针对近似非齐次指数律的非等间距序列预测问题,提出了一种非等间距NGM(1,1,k)模型.为进一步提高模型的预测精度,利用线性插值方法对模型的背景值进行重构,以平均相对误差最小化为目标,建立了关于插值系数的优化模型,并运用穷举算法确定模型的最优插值系数.最后通过两个实例表明了非等间距NGM(1,1,k)模型及其优化模型的有效性和实用性.
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| 关 键 词： | 灰色系统 非等间距序列 NGM(1,1,k)模型 非齐次指数序列 |
Non-equidistant NGM(1,1,k) Model and Its Application |
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| LI Ya-nan,ZENG Liang. Non-equidistant NGM(1,1,k) Model and Its Application[J]. Mathematics in Practice and Theory, 2017, 0(9): 159-165 |
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| Authors: | LI Ya-nan ZENG Liang |
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| Abstract: | In view of the prediction problems of the non-equidistant sequence which obeyed non-homogenous exponential rule,a non-equidistant NGM (1,1,k) model is proposed.To further improve the prediction accuracy of the model,its background value is reconstructed by using linear interpolation method,then an optimization model is constructed with the objective of minimum average relative error in order to optimize the interpolation coefficient,and the optimization value of interpolation coefficient is determined by using exhaustive algorithm.Finally,two examples illustrate the validity and practicability of the non-equidistant NGM (1,1,k) model and its optimization model. |
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| Keywords: | grey system non-equidistant sequence NGM(1,1,k)model non-homogenous exponential sequence |
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