基于三次Bézier基函数插值的GM(1,1)模型背景值优化研究
OPTIMIZATION OF BACKGROUND VALUE IN GM (1, 1) BASED ON CUBIC BéZIER BASIS FUNCTION INTERPOLATION

本文研究了传统灰色GM（1，1）模型存在模型精度不高的问题.利用带形状参数的三次Bézier基函数，给出插值函数的表达式，并结合复化梯形公式，给定误差限的方法，获得了比传统灰色GM（1，1）模型更高精度的结果.推广了传统灰色GM（1，1）预测模型的结果.
In this paper, we study the accuracy of GM(1,1) forecasting model. In combination with compound trapezoid formula, cubic Bézier basis function method with shape parameter interpolation function expression is presented to solve the problem of low precision of traditional GM(1,1). Given error limits, the model which given in this paper can obtain more precision than traditional GM(1,1) model, which enlarge the application scope of GM(1,1) model