基于矩阵条件数的NGM(1, 1, k) 模型病态性研究

针对灰色NGM(1,1,k)模型的病态性问题,以矩阵谱条件数作为测量其病态性的工具,对该模型背景值在不同取值下的系数矩阵谱条件数分类进行了分析与证明.研究结果表明,当且仅当系统原始数据序列为常数列时,NGM(1,1,k)模型才会出现严重病态性问题,而此时进行灰色预测建模毫无实际意义.最后通过实例对该模型的病态性进行了实验分析.研究结论认为,通常情况下灰色NGM(1,1,k)模型并不存在严重病态性问题.

Study on morbidity of NGM(1, 1, k) model based on conditions of matrix

With regard to the morbidity of NGM(1,1,??) model, this paper takes the conditions of matrix as a tool to measure
the morbidity of the model and analyzes the value of conditions of coefficient matrix with the background value of this model
in three different cases, respectively. The results show that only when the original data sequence is a nonnegative constant
one, this model appears to be a serious morbid problem. However, in this case, the grey prediction modeling is meaningless.
Finally, an illustrative example is adopted for demonstration. The study conclusion shows that NGM(1,1,??) model has no
morbidity.