Gauss-Seidel Progressive and Iterative Approximation for Least Squares Fitting

Progressive-iterative approximation (PIA) is an efficient method for data fitting that attracts the attention of many researchers and has a wide range of applications. However, the convergence rate of LSPIA is prolonged. In this study, we design a fast PIA format based on the Gauss-Seidel iterative method named Gauss-Seidel progressive and iterative approximation for least squares curve and surface fitting (GS-LSPIA). Firstly, the control points of the fitting curve (surface) are selected from the given data points.