关于非等距序列建模过程的讨论

Discussion on Modeling Non-equidistance Sequence

目的:怎样建立非等距序列的最佳数学模型.方法:讨论用灰色系统GM(1.1)模型和非线性回归方法建立非等距序列的数学模型的过程,找出产生问题的原因,寻求解决问题的方法.结果:接近于指数规律变化的非等距序列,用非线性回归方法建立的数学模型比用灰色系统GM(1.1)模型方法建立的数学模型的精度高;对于其他的非等距序列,用灰色系统GM(1.1)模型方法建立的数学模型比用非线性回归方法建立的数学模型的精度高.结论:在建立非等距序列的数学模型时,采用灰色系统GM(1.1)模型方法与非线性回归方法结合的策略,可以得到较佳的数学模型.

Objective： How to set up the best mathematical model of non-equidistance sequence. Methods： By discussing procedure that the grey system GM（1.1） model method and the non-linear regression method set up mathematical model, find reason of produce problem and find method that solve problem. Result： For the non-equidistance sequence that is close to exponential function, the non-linear regression method has done better than the grey system GM （1. 1） model method; for the non-equidistance sequence that is not close to exponential function, the grey system GM （1. 1） model method has done better than the non-linear regression method. Conclusion： In setting up mathematical model for the non-equidistance sequence, we could get better mathematical model by taking the grey system GM（1.1） model method and the non-linear regression method together.