加权对差法的本质

The Essence of the Weighted Symmetrical Subtraction

加权对差法是传统逐差法的一种改进方法。通过与基于线性变化规律的最小二乘法计算式相比,本文发现加权对差法就是最小二乘法的一个实现,因此加权对差法对该类数据是最优的。然而,对匀加速直线运动的实验数据,因其模型不符合线性变化规律,故无论逐差法还是对差法,都不是最优的。

The weighted symmetrical subtraction algorithm is an improved method over the conventional seriatim subtraction algorithm. Compared with the least square error（ LSE） scheme on the data following linearly varying rule,it is found that the weighted symmetrical subtraction is nothing but a realization of LSE. As a result,the weighted symmetrical subtraction algorithm is the best for such kind of experimental data. However,since the experimental data of motion with uniform acceleration in a straight line do not a linearly varying rule,both the seriatim subtraction and symmetrical subtraction are not optimal.