Generalized and optimal sequence of weights on a progressive-iterative approximation method with memory for least square fitting

The generalized and optimal sequence of weights on a progressive-iterative approximation method with memory for least square fitting (GOLSPIA) improves the MLSPIA method by extends to the multidimensional data fitting. In addition, weights of the moving average are varied between iterations, using the three optimal sequences of weights derived from the singular values of the collocation matrix. It is proved that a series of data fitting with an appropriate alternative of weights converge to the solution of least square fitting. Moreover, the convergence rate of the new method is faster than that of the MLSPIA method. Some examples and applications in this paper show the efficiency and effectiveness of the GOLSPIA method.