New information multivariable optimization MGM(1,n) model with non equidistance and based on background value optimization

The function with non-homogeneous exponential law, based on index characteristic and integral characteristic of grey model GM(1,1), was used to fit the one-time accumulated sequence, and the formula of background value was given, aiming at the problem of lower precision as well as lower adaptability in non-equidistant multivariable model MGM(1,n). A new information optimization model MGM(1,n) with non equidistance and multi variable based on background optimization was put forward, took the m-th component of the original sequence as initial condition, the mean relative error as objective function, and the modified one of initial value and the parameters of background value as design variables. This proposed MGM(1,n) model can be used in equidistance & non-equidistance modelling with higher precision as well as stronger adaptability. Examples have validated the practicability and reliability.

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