中文摘要：

分析了GM（1,1）模型中信息矩阵产生病态的原因,提出调整实测数据计量单位来降低信息矩阵的条件数。根据GM（1,1）模型原理,证明了调整实测数据计量单位不会影响模型的相对残差、平均残差及预测精度。数值实验分析结果表明,调整计量单位法是一种简单、易实现且精确解决GM（1,1）模型病态问题的实用方法。

英文摘要：

Ill-posed problems exist in the gray system GM （1,1） model. Seriously ill-posed information matrices will occur in larger original measured data values. Reasons which cause ill-posed information matrices in GM （1,1） modesl are analysized in detail. A method to adjust the measurement unit of the original 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. Numerical experiments and analysis demonstrate that this method of adjusting the measurement unit algorithm for a GM （1, 1） model is easy to implement, simple, accurate, and widely applicable.