Weighted progressive iteration approximation and convergence analysis

We present a new and efficient method for weighted progressive iteration approximations of data points by using normalized totally positive bases. Compared to the usual progressive iteration approximation, our method has a faster convergence rate for any normalized totally positive basis, which is achieved by choosing an optimal value for the weight. For weighted progressive iteration approximations, we prove that the normalized B-basis of a space provides the fastest convergence rate among all normalized totally positive bases of the space. These results are also valid for tensor product surfaces.