DFP Optimization Method for Progressive Iterative Data Points Fitting

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.