  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.
