Optimizationand Its Application Of GM(1,1) Model Based On Numerical Analysis Theory

The grey system theory is uncertain system,it is mainly developed to study uncertainties of "small samples" and "poor information".Its application of a small amount of information and uncertainty problems research has a good advantage.As an important part of grey system theory,grey forecast model is one of the most important research part of it.and the grey GM(1,1)model is the most widely used in grey forecasting model.Therefore,in order to improve the grey GM(1,1)model simulation and forecast accuracy,it is meaningful to research on grey forecast model.Firstly,we analyze the modeling mechanism of the original GM(1,1)model and the origin of the error in this paper,and the formula of background value is one of the main factors causing systematic error of GM(1,1)model.Thereby,based on the numerical analysis theory,to improve the integral of the background value,on the basis of existing dynamic sequence model,combined with compound Simpson quadrature formula,optimize the background value of the model to improve the accuracy of the model.Secondly,the GM(1,1)model is optimized based on the third-order and fourth-order Runge-Kutta method in the one-step method.A new parameter method is proposed to optimize the parameter identification in the model,and discussed the influence on the accuracy of development coefficient change of the two optimization models.Then based on fourth-order Adams explicit formulas and implicit formulas in linear multistep methods to optimize the GM(1,1)model,and compared the trend of the error with the development coefficient and its scope of application in the two methods.And then compared the similarities and differences between the single-step and multi-step optimization of GM(1,1)model,make the GM(1,1)model is better applied to practical problems,and expand the applicability of the model.Finally,three models optimized are applied to the total energy consumption,crude oil production and gross domestic product.It is proved that the method proposed has higher accuracy and better results,with the advantages of universality,accuracy and efficiency.