摘要
为进一步提高GM(1,1)模型的建模效率,提出了一种新的GM(1,1)模型,从以下方面进行了改进:第一,基于重心权有理插值,改进了背景值的重构质量;第二,基于单纯形法,优化了模型的初始条件;第三,使用非线性最小二乘拟合,进一步优化了模型的参数.最后,通过数值模拟和具体实例进一步验证方法的有效性.
To further improve modeling efficiency of GM(1,1),we propose a new GM(1,1)model,which include the following aspect:Firstly,reconstruction quality for the background value is improved by the barycentric rational interpolation,which overcomes the defect of existing method.Secondly,the initial condition is optimized by simplex method(SM).Thirdly,using nonlinear least squares(NLS),the parameters are further optimized.In the end,simulation and practical examples are presented to further verify the effectiveness of proposed approaches.
作者
荆科
刘业政
康宁
JING Ke;LIU Ye-zheng;KANG Ning(School of Management,Hefei University of Technology,Hefei 230009,China;School of Mathematics and Statistics,Fuyang Normal University,Fuyang 236037,China;School of Economics,Fuyang Normal University,Fuyang 236037,China)
出处
《数学的实践与认识》
北大核心
2018年第24期75-82,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(71501057)
阜阳师范学院自然科学研究重点项目(2017FSKJ02ZD)
阜阳师范学院青年人才基金重点项目(rcxm201707,rcxm201711)
关键词
重心权有理插值
背景值
GM(1
1)模型
单纯形法
初始条件
barycentric rational interpolation
background value
GM(1,1)model
Simplex method:initial condition
