Study on the optimum prediction model for GM

GM model is the core of grey system theories. It has been widely applied to social, economic, agriculture, industrial and many other fields. It has solved lots of problems of scientific and technology. In 1982, professor Ju Long Deng published the first research paper about the grey systems, and established GM(1.1). Many scholars have improved it since then, and a series of prediction models have been established, the literature on GM is now voluminous, such as DMG, Verhulst and so on. All the models make an optional data of the raw sequence as background condition,they all look one data as the system\´s real value, these man-made conditions may led to the inexact in the simulation and prediction of the time response sequence, because they have many occasional factors. In order to prove the precision of these models,in this paper , we think that all the system\´s initial data must not be ignored , all of them can affect the system, then we develop a new model, after the development coefficient and the grey action quantity are given, we utilize "the least square" to find the constant number in the common solution of GM in this paper, then, gain an optimum time response sequence.In this paper we also proved that the optimum GM(1,1) is the best-fit line and it has superior precision in simulation and forecasting than traditional one. So, this paper has high value on theory and application.