Progressive Iterative Approximation Method with Memory and Sequences of Weights for Least Square Curve Fitting - Saknarin Channark; Poom Kumam; Parin Chaipunya; Wachirapong Jirakitpuwapat (Science & Technology Asia, 2023)
The progressive iterative approximation method with memory and sequences of weights for least square curve fitting (SSLSPIA) is presented in this paper. This method improves the MLSPIA method by varying the weights of the moving average between iterations, using three sequences of weights derived from the singular values of a collocation matrix. It is proved that a sequence of fitting curves with an appropriate alternative of weights converge to the solution of least square fitting and that the convergence rate of the new method is faster than that of the MLSPIA method. Some examples and applications in this paper prove the SSLSPIA method is superior.