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 and Lin (2014) under the same assumption. Examples verify this phenomenon.

在本文中，我们提出了一种具有最小二乘拟合记忆（MLSPIA）的渐进和迭代逼近方法。它迭代地调整控制点和加权总和，以构建具有三个权重的一系列拟合曲线（曲面）。对于任何归一化的完全正的基础，即使当搭配矩阵的列秩不足时，我们也可以获得确保这些曲线（表面）收敛到给定数据点的最小二乘拟合曲线（表面）的条件。在相同假设下，Deng和Lin（2014）证明了该方法的理论收敛速度快于最小二乘拟合（LSPIA）的渐进和迭代逼近方法之一。实例证明了这种现象。