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In this paper, we propose a new SSOR-like method with four parameters to solve the augmented system. And we analyze the convergence of the method and get the optimal convergence factor under suitable conditions. It is proved that the optimal convergence factor is the same as the GMPSD method [M.A. Louka and N.M. Missirlis, A comparison of the extrapolated successive overrelaxation and the preconditioned simultaneous displacement methods for augmented systems, Numer. Math. 131(2015) 517-540] with five parameters under the same assumption.

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In this paper, we present a progressive and iterative approximation method with memory for least square fitting (MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. For any normalized totally positive basis even when the collocation matrix is of deficient column rank, we obtain a condition to guarantee that these curves (surfaces) converge to the least square fitting curve (surface) to the given data points. It is proved that the theoretical convergence rate of the method is faster than the one of the progressive and iterative approximation method for least square fitting (LSPIA) in [Deng C-Y, Lin H-W. Progressive and iterative approximation for least squares B-spline curve and surface fitting. Computer-Aided Design 2014;47:32-44] under the same assumption. Examples verify this phenomenon.