| 同时优化背景值和灰导数的新非等间距GM(1,1)模型 |
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| 引用本文： | 雍华,魏勇,孔新海.同时优化背景值和灰导数的新非等间距GM(1,1)模型[J].数学的实践与认识,2011,41(20). |
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| 作者姓名： | 雍华 魏勇 孔新海 |
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| 作者单位： | 西华师范大学数学与信息学院,四川南充,637002 |
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| 基金项目： | 四川省教育厅重点资助课题(2006A077); 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) |
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| 摘 要： | 结合GM(1,1)的建模过程,提出了以原始序列的一次累加生成序列为背景值的非等间距序列GM(1,1)模型的最原始形式;并基于灰模型的非齐次指数特性和求导的定义,从灰导数在离散点的生成出发,同时优化最原始的非等间距灰微分方程的灰导数和背景值,并建立新非等间距灰模型;新模型不仅提高了灰模型的拟合精度和预测精度,且拓宽了GM(1,1)的适用范围.
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| 关 键 词： | GM(1 1) 非齐次指数 求导 背景值 灰导数 优化 |
One New Non-equidistance GM(1,1) Optimized the Grey Derivative and the Background Value at the Same Time |
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| YONG Hua,WEI Yong,KONG Xin-hai.One New Non-equidistance GM(1,1) Optimized the Grey Derivative and the Background Value at the Same Time[J].Mathematics in Practice and Theory,2011,41(20). |
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| Authors: | YONG Hua WEI Yong KONG Xin-hai |
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| Institution: | YONG Hua,WEI Yong,KONG Xin-hai (College of Mathematics and Information,China West Normal University,Nanchong 637002,China) |
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| Abstract: | Through combine the process of modeling GM(1,1),this article puts forward the non-equidistance series' GM(1,1) model's primitive form by making the primitive series' 1-AGO series be the background value.Based on grey model's non-odd order exponential trait and the definition of derivation calculus,this paper begins with generation of the derivative at discrete points,optimizes the grey derivative and background value of the primitive non-equidistance GM(1,1) at the same time.Then,establish a new non-equidis... |
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| Keywords: | GM(1 1) non-exponential trait derivation calculus background value grey derivative optimize |
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