非等间距直接GM（1，1）模型及其优化

NON-Equidistant GM （1, 1） Direct Model and Its Optimization

针对非齐次指数形式的非等间距序列，提出了非等间距GM（1，1）直接建模模型，并在此基础上将同时优化背景值和灰导数与利用平均相对误差最小确定响应系数的方法相结合，建立了新的非等间距GM（1，1）直接建模模型。并通过实例分析说明了优化的新模型的可行性和有效性。

According to the non-equidistant sequence in non-homogeneous index form, the non-equidistant GM（1,1） direct model was constructed by the original sequence. And the new non-equidistant GM（1,1） direct model was established by combining simultaneous optimization of background value and grey derivative with using ＂average relative error minimum＂ to determine the response coe^cient. Through analyzing the examples, it illustrates the feasibility and effectiveness of the new optimization model