Stability of GM(1,1) power model on vector transformation.

The morbidity problem of the GM(1,1) power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM(1,1) power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM(1,1) power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM(1,1) power model. [ABSTRACT FROM AUTHOR]