基于遗传算法的三次样条函数拟合

Genetic Algorithms Based Cubic Spline Functions Fitting

介绍了遗传算法 (GA)的一种新应用——三次样条函数拟合中的参数估计问题。三次样条函数拟合是曲线拟合的一个公认的较好方法 ,它具有很好的分段光滑性 ,但三次样条函数拟合涉及到矩阵求逆 ,离散样本点越多 ,矩阵就越大 ,求逆就越繁琐。文中将 GA用于三次样条函数拟合的系数求解 ,避开了矩阵求逆的繁琐问题 ,结合具体例子作了一些探索。文中还对标准遗传算法进行了适当的改进 ,实验结果说明遗传算法是用于参数估计、优化的有力工具。

A new application to parameter estimation in cubic spline function fitting via genetic algorithms (GA) is presented. Cubic spline functions fitting is a good method in the curve fitting because they are characterized by very good subsection smoothness. But in cubic spline function fitting the inverse of the matrix must be made. The more discrete the sample data are, the larger the matrix is and the more complicated its inverse is. GA is used to obtain coefficients of cubic spline function fitting to avoid the inverse of the matrix and some work is made with an example. Suitable improvements are also made for the standard GA. The experimental results show that GA is powerful for parameter estimation and optimization.