Adjust Measurement Unit Algorithm for Ill-posedProblem of GM(1,1) Model

Objective Ill-posed problems exist in the gray system GM(1,1)model.Seriously ill-posed informationmatrices will occur in larger original measured data values.Reasons which cause ill-posed informationmatrices in GM(1,1)modesl are analysized in detail.A method to adjust the measurement unit of theoriginal measured data values to reduce the conditional number of information matrices is put forward.Based on GM(1,1)model theory,we show that an adjustment to the measured data units of measure-ment does not affect the model relative residuals,average residuals,or prediction accuracy.Numericalexperiments and analysis demonstrate that this method of adjusting the measurement unit algorithmfor a GM(1,1)model is easy to implement,simple,accurate,and widely applicable.