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

On a progressive and iterative approximation method with memory for least square fitting