曲线拟合的最小一乘法

最小一乘法的解,由于存在着绝对值方程而不便于计算,成为困扰数理界200多年悬而未决的难题.基于对最小一乘准则下各种数学模型的大量计算和长期研究后发现,若存在最小一乘最佳参数a=a*∈Rn使绝对偏差值和为极小的最小一乘准则im=∑1 yi-f(xi,a*)=min成立,则拟合函数f(x,a*)的表征为:至少存在n个点x1,x2,…,xn,使yi-f(xi,a*)=0,i=1,2,…,n(n≤m)成立,从而最小一乘解可以实现.

Least Absolute Deviation Method of Curve Fitting

The solution of least absolute deviation(LAD),a pending problem for more than 200 years in mathematics,is not easy to calculate because of the absolute value function.Based on a great deal of computing and long-term study of various mathematical models under LAD criteria,a conclusion is drawn that if there is a LAD parameter a=a*∈Rn,and making the following LAD criterion tenable ∑mi=1|yi-f(xi,a*)|=min,then the fitting function f(x,a*) can be characterized that there are at least n points x1,x2,…,xn,making yi-f(xi,a*)=0,i=1,2,…,n(n≤m) valid,the problem of LAD solution can be achieved.