DFP优化的数据点渐进迭代拟合方法  

DFP Optimization Method for Progressive Iterative Data Points Fitting

作　　者：张莉[1] 赵志远 葛先玉 张能俊 姚红丽 檀结庆[1,2] Zhang Li;Zhao Zhiyuan;Ge Xianyu;Zhang Nengjun;Yao Hongli;Tan Jieqing(School of Mathematics,Hefei University of Technology,Hefei 230009;School of Computer and Information,Hefei University of Technology,Hefei 230009)

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]合肥工业大学计算机与信息学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2020年第2期233-238,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61472466,61100126)

摘　　要：DFP方法(由Davidon,Fletcher和Powell 3人共同提出)是求解无约束优化问题的一种经典方法,文中指出数据点的拟合问题可转化为无约束优化问题的求解,并基于DFP优化方法给出了一种大规模数据点拟合方法,称之为DFP渐进迭代拟合方法.文中证明了该方法生成的极限曲线为初始数据点的最小二乘拟合曲线;它承袭了经典最小二乘渐进迭代逼近算法的众多优良性质,如具备直观的几何意义、可灵活地拟合大规模数据点、初始控制顶点的选择不影响最终迭代结果等.数值实例进一步表明,同等条件下,文中方法的收敛速度明显优于现有的几种数据点拟合方法.DFP method(proposed by Davidon,Fletcher and Powell)is a classical method for solving unconstrained optimization problem.Actually,data point fitting problem can be transformed into the solution of unconstrained optimization problem.Considering this,one new fitting method for large-scale data points is proposed based on DFP optimization method,which is called DFP progressive iterative fitting method.It is proved that the limit curve generated by the presented method is least square fitting curve of the initial data point.It inherits all the nice properties of the classical least square progressive iterative approximation algorithm,such as intuitive geometric significance,flexible fitting of large-scale data points,and arbitrary choosing of initial control vertices.Numerical examples further show that the presented method’s convergence rate is better than those of the other existing data point fitting methods under the same terms.

关 键 词：渐进迭代逼近 DFP优化方法 B样条 曲线拟合 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]