| 近非齐次指数序列GM(1,1)模型灰导数的优化 |
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| 引用本文： | 陈芳,魏勇.近非齐次指数序列GM(1,1)模型灰导数的优化[J].系统工程理论与实践,2013,33(11):2874-2878. |
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| 作者姓名： | 陈芳 魏勇 |
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| 作者单位： | 1. 西华师范大学 数学与信息学院, 南充 637002;
2. 泸州职业技术学院基础部, 泸州 646005 |
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| 基金项目： | 四川省应用基础研究项目(2008JY0112);四川省高等教育人才培养质量和教学改革项目(P09264);四川省留学人员科技活动择优资助项目(川人社函2010年32号) |
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| 摘 要： | 从原始序列为非齐次指数律的GM(1,1)的灰导数出发,利用向前差商和向后差商的加权平均值作为GM(1,1)的灰导数白化值, 并给出了加权系数λ的具体表达式,进而建立了优化灰导数后适用于原始序列为非齐次指数律的GM(1,1)模型,且证明了此模型具有白指数律重合性,给出了求 参数的方法及表达式,并通过实例对比验证了此模型具有更高的精度,并且对于严格的非齐次指数序列能够完全的拟合.
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| 关 键 词： | 非齐次指数模型 GM(1 1) 灰导数 白指数律 |
| 收稿时间： | 2011-11-15 |
Approximate non-homogeneous index sequence GM(1,1) model of grey derivative optimization |
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| CHEN Fang,WEI Yong.Approximate non-homogeneous index sequence GM(1,1) model of grey derivative optimization[J].Systems Engineering —Theory & Practice,2013,33(11):2874-2878. |
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| Authors: | CHEN Fang WEI Yong |
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| Institution: | 1. College of Mathematics and Information, China West Normal University, Nanchong 637002, China;
2. Department of Basic, Luzhou Vocational and Technical College, Luzhou 646005, China |
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| Abstract: | Based on the original sequence for non-homogeneous exponential of the grey derivative of GM(1,1) model, this paper uses forward difference quotient and backward difference quotient of the weighted average as the grey derivative of the GM(1,1) model, and gives the concrete expression of the weighted coefficient λ to establish the new optimized grey derivative of GM(1,1) model, which adapts to the non-homogenous exponential sequence. This paper proves that this model possesses white exponential law coincidence, gives a method to solve parameters and gets expression of parameters. The examples show this model has higher precision and can completely fit for strict non-homogeneous index series. |
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| Keywords: | non-homogeneous exponential model GM(1 1) model grey derivative white exponential law |
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