反求参数与曲线拟合

Counter Seeking parameters and Curve Fitting

将点列（ｒ０，ｙ０），（ｘ１，ｙ１），…，（ｘｎ，ｙｎ）作为未知参数的二阶线性微分方程Ｃａｕｃｈｙ问题的观测值，利用待定边值的三次样条函数及最小二乘法反求参数，然后以Ｃａｕｃｈｙ问题的解作为已知点列的拟合曲线．这是对［１］中ＧＭ（２，１）模型的重要改进．是一类适用范围很广的曲线拟合法．经过实算说明这个方法具极高的拟合精度．

This paper presents a new method for fitting a curve.This method takes the givcn set of points(xi,yi)i=0,1..., n as observed values of the solution of a second order linear ordinary differential equation with unknown parameters,then uses the cubic splines with undctcrmined boundary values as well as the least-square method to determinc thew paramctcrs in the equation.Finally,the solution of the Cauchy problem is taken as the fitting curve.This method can be considered as a significant improvement of model GM(2,1)in[1].Computational results show that it is a good fitting method with high prccisions.