基于向量变换的DGM(1,1,k~α)模型的病态性

Morbidity of DGM(1,1,k~α) Model Based on Vector Transformation

系数矩阵谱条件数是度量灰色预测模型病态性的重要工具，而向量的数乘变换和旋转变换是降低系数矩阵谱条件数的有效方法．首先，利用向量的数乘变换和旋转变换研究DGM（1，1，k^α）模型的病态性，结果显示，DGM（1，1，k^α）模型的病态性主要受系数矩阵列向量的长度之比、夹角大小及时间幂的影响；其次，给出了基于向量变换的DGM（1，1，k^α）模型病态性的解决步骤；最后，通过一个算例验证了向量变换在解决矩阵病态性问题时的有效性和实用性．

The precondition number of the coefficient matrix is an important tool to measure the morbidity of grey prediction model, and the multiplication transformation and rotation transformation of vectors are effective methods to reduce the precondition number of the coefficient matrix. Firstly, the morbidity of DGM （1, 1, k^α） model is studied by means of vector multiplication and rotation transformation, the results show that the condition number of the matrix is influenced by the length ratio, Angle size and time power of matrix column vectors. Secondly, based on vector transform, the solution of the morbidity of DGM （1, 1, k^α） model is given. Finally, A numerical example is given to demonstrate the effectiveness and practicability of the vector transformation in solving the morbidity of matrix.