Nonlinear Optimization of GM(1,1) Model Based on Multi-parameter Background Value

Abstract : By studying the existing algorithms for background value in GM(1,1), a nonlinear optimization model of GM(1,1) based on multi-parameter background value is given. The paper uses the invertible matrix of the parameter to optimize and estimate the parameters $\hat{a}$; in addition, the parameter estimate $\hat{a}$ obtained from the multi-parameter background value has higher prediction accuracy, thus overcoming the restriction on the prediction based on the fixed average background value in other literatures. the simulated values obtained by the optimized model (NOGM(1,1)) are more precise, and the maximum error is reduced by 15%. The nonlinear optimization model of GM(1,1) based on multi-parameter background value provides algorithms for further study of GM(1,1) model.