| 反求参数与曲线拟合 |
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| 引用本文： | 孙韫玉.反求参数与曲线拟合[J].武汉大学学报(工学版),1994(1). |
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| 作者姓名： | 孙韫玉 |
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| 作者单位： | 武汉水利电力大学基础科学系 |
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| 摘 要： | 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．
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| 关 键 词： | 曲线拟合 微分方程 三次样条函数 最小二乘法 最优化算法 |
Counter Seeking parameters and Curve Fitting |
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| Sun Yunyu.Counter Seeking parameters and Curve Fitting[J].Engineering Journal of Wuhan University,1994(1). |
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| Authors: | Sun Yunyu |
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| Affiliation: | Department of Basic Sciences |
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| Abstract: | 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)in1].Computational results show that it is a good fitting method with high prccisions. |
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| Keywords: | curvc fitting diffirential cquation cubic spline least-square computational method of optimization |
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