Stepwise iteration and optimization scheme for data fitting based on non-uniform B-spline

A stepwise iteration and optimization fitting method for handling large scale data points has been presented in this paper. By iteratively adjusting the control points, a set of fitting curves are produced with obviously geometric meaning. Negative gradient direction has been chosen as the descent direction in order to minimize the distances between the initial points and corresponding points of the fitting curves. With given precision, the total iteration steps can be estimated. It is proved that the given method is convergent, and the limit curve is the least square fitting curve for the initial data. Numerical examples and comparisons are also given to show effectiveness and flexibility of the method.