The Morbidity Problem of GM(2,1) Model Based on Vector Transformation

摘要

This paper applies multiple and rotation transformation of vectors to discuss the morbidity problem of GM(2,1) model in the parameter identification processing. Firstly, we analyze the factors which affect the condition number of special matrix, and get the result that the condition number relate to the ratio of length and the included angle of column vector So we can adjust the special matrix to be a well-conditioned one by multiple transformations for the ratio of length and by rotation transformation for the included angle respectively. Then, we study the morbidity problem of GM(2,1) model by vectors transformation. We convert a 3-order matrix to a 2-order matrix by using equalization to convert a 3-order matrix into a block diagonal matrix. To a 2-order matrix, we do multiple transformations of vectors for its ratio of length and do rotation transformation of vectors for its included angle. Finally, the calculation steps of the parameters is given and a numerical results show that this method can perfectly solve the morbidity problem of GM(2,1) model