分数阶累加灰色预测模型的探讨_吴利丰.pdfVIP

210016 Grey model based on fractional order accumulate Wu Lifeng, Liu Sifeng Nanjing University of Aeronautics and Astronautics Nanjing,College of Economics and Management,210016(E-mail:wlf6666@126. com) Abstract—Why grey model is suitable for small sample is explained. Take discrete grey model as an example, based on matrix perturbation theory, we prove that the larger sample, the bigger perturbation bound and the smaller sample, the smaller perturbation bound under the equal perturbation when we use the traditional grey first order accumulate. The fractional order accumulate grey model is defined in order to reduce perturbation bound and its availability and practicality are verified by an example. Keywords—grey system, discrete grey model, small sample, perturbation analysis 1  T 1 T   2   (B B ) B Y 1   1 x (1) (1)  x (1) (2)  B 1 x (1) (2)  Y x (1) (3)  ,        (1)   (1)  1 x (n 1)  x (n ) 