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中国管理科学

中国管理科学 ›› 2001, Vol. ›› Issue (5): 38-44.

• 论文 • 上一篇    下一篇

GM模型的病态性问题

郑照宁, 武玉英, 包涵龄   

  1. 北京工业大学经济与管理学院, 北京, 100022
  • 收稿日期:2000-11-03 出版日期:2001-10-28 发布日期:2012-03-06
  • 基金资助:
    国家自然科学基金资助项目(7970004);北京工业大学星火科技基金资助项目(XH-2000-26-YJ)

Morbidity Problem in Grey Model

ZHENG Zhao-ning, WU Yu-ying, BAO Han-ling   

  1. School of Economics and Management, Beijing Polytechnic University, Beijing 100022, China
  • Received:2000-11-03 Online:2001-10-28 Published:2012-03-06

PDF (PC)

2060

被引次数

73

摘要： 本文指出GM模型的方程组存在着严重的方程病态性问题,探讨了GM模型产生病态的原因:(1)矩阵由累加数构成,累加数之间有较大的数量级差别;(2)GM模型中的蜕化使矩阵中元素数量级差别过大;(3)GM模型的矩阵生成方式使得我们难以降低方程组的病态性。并对一个被广泛引用的算例进行了分析。最后,我们认为必须小心使用GM模型。

关键词: GM模型, 条件数, 范数, 病态方程组, 病态矩阵, 方程组的病态性, 摄动分析

Abstract: This paper points out that the sysstem of equations of grey model(GM model)has very serious morbidity problem We discuss the reasons why GM model has morbidity problem:1)Matrices are composed of accumulating numbers which have very large scalar difference among them;2)Degeneration in some grey model makes very large scalar difference among elements of matrices;3)The way to build matrices in grey model let us hardly reduce morbidity of the system of equations A widely referrenced example is analyiedin this paper At the end,we suggest that it must be careful to use grey model.

Key words: grey model, condition number, norm, illed system of equations, illed matrix, morbidity, perturbation analysis

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