基于轉(zhuǎn)換經(jīng)濟數(shù)據(jù)統(tǒng)計計量單位的灰色系統(tǒng)病態(tài)問題解決方法

摘要： 在對經(jīng)濟統(tǒng)計數(shù)據(jù)分析時,采用灰色系統(tǒng)模型會存在病態(tài)問題。文章討論了GM(1,1)模型中矩陣產(chǎn)生病態(tài)的原因,提出轉(zhuǎn)換經(jīng)濟數(shù)據(jù)統(tǒng)計計量單位的方法來降低病態(tài)矩陣的條件數(shù)。數(shù)值試驗分析表明,轉(zhuǎn)換經(jīng)濟數(shù)據(jù)統(tǒng)計計量單位可以很好地解決以條件數(shù)大小為判斷標(biāo)準(zhǔn)的灰色系統(tǒng)模型的矩陣病態(tài)問題。
Ill-posed problem exists in gray system GM( 1,1) model in the field of economic statistics and analysis.Larger economic statistics data value always leads to ill-posed information matrix. This paper analyzed the reasons which caused ill-posed matrix in GM( 1,1) model and put forward converting economic data statistical measurement unit to reduce the condition number of the matrix. Analysis of the numerical experiments showed that converting economic data statistical measurement unit could be a good solution for the ill-posed matrix of grey system model which deemed the condition number as the criteria for judging.