Improvement and Application of Initial Value of Non-equidistant GM(1,1) Model

Aiming the problem of determining initial value of nonequidistant GM(1,1) model, in the basis of analyzing modelbuilding mechanism of non-equidistant GM(1,1) model, the cause of the problem was found out and a new method for initiating values of non-equidistant GM(1,1) model was proposed to minimize the quadratic sum of its fitting error. Based on index characteristic of grey model and the definition of integral, the discrete function with non-homogeneous exponential law was used to fit the accumulated sequences, new constructing method of the background value was put forward and formula of background value was given. Combining the proposed formula of background value, the formula of initiating value was detruded. The new non-equidistant GM(1,1) model with the proposed formula of initiating value has the characteristic of high precision as well as high adaptability. Examples validate the practicability and reliability of the proposed model.