灰色Verhulst预测模型的病态特性

为揭示灰色Verhulst模型的建模精度在原始序列存在微小扰动下的变化规律，采用矩阵谱条件数作为研究工具对该模型系数矩阵谱条件数的取值进行分类讨论. 研究结果表明，当且仅当系统原始数据序列第一项为大于零的常数，其他所有项数据皆为0时，建立灰色Verhulst模型才会呈现严重病态性，而采用已呈现特定规律的数据序列构建灰色Verhulst预测模型毫无实际意义. 研究结论认为，灰色Verhulst模型并不存在严重病态性.

Study on morbidity of grey Verhulst forecasting model

Aiming to reveal the changing law of modeling accuracy of grey Verhulst model resulted from the small perturbation of primitive sequence, we took the spectrum condition number of matrix as a tool of measuring the morbidity of this model and analyzed the value of conditions of coefficient matrix. The research result shows that only when the first data point of original data sequence be a constant (constant >0) and the rest of data points be all 0, this model will appear to be a serious morbid problem, however, at this time, it is meaningless to build a grey Verhulst model by using a raw data sequence with an inherent law for prediction. The research conclusion suggests that grey Verhulst model has no morbidity.