摘要
针对GM(1,1)模型对上凸序列建模时会出现误差较大的情况进行了研究.首先分析了GM(1,1)对上凸序列建模时的残差变化规律,然后通过分析得出了残差变化规律的精确描述,同时证明了残差序列的几个性质定理.基于残差序列的性质定理提出了基于上凸序列建模的残差修正GM(1,1)模型.将新模型与多种改进的GM(1,1)模型进行对比,实证结果表明新模型具有很高的模拟预测精度,并且适用于一切上凸序列的建模.
The issues of large errors of GM（1,1） model for concave sequence modeling have been studied in this paper. The characters of residuals of GM（1,1） model built on concave sequence have been analyzed, and precise description of the residuals have been obtained,along with several important theorems. Based on these theorems, the improved GM（1,1）model based on residual modification for concave sequence modeling has been proposed. The new model has been compared to the other improved models, and the results show that the accuracy of the new model is very high, and it is applicable for all concave sequence modeling.
作者
孔新海
马新
KONG Xin-hai MA Xin(School of Intelligent Maufacturing and Energy Engineering, Guang＇an Vocational Technical College, Guang＇an 638000, China School of Science, Southwest University of Science and Technology, Mianyang 621010, China)
出处
《数学的实践与认识》
北大核心
2017年第19期257-264,共8页
Mathematics in Practice and Theory
基金
四川省教育厅基金项目(14ZB0388)
