A family of hybrid iterative approximation methods for fitting blending curves

Data fitting is a fundamental research problem in many scientific fields. The progressive iterative approximation for least-squares fitting is an effective method for fitting many data points, because of its simple iterative algorithm and intuitive operation. We combine an iterative method for computing Moore–Penrose generalized inverse with the classical progressive iterative approximation for least-squares fitting method to construct a family of accelerated iterative methods for fitting curves to data. The resulting iterative curve sequence converges to the least-squares fitting result for the given data set. We prove that the proposed method has faster average convergence rate and asymptotic convergence rate than previous methods. Some numerical examples illustrate the feasibility and efficiency of our method.