曲线拟合的最小一乘法

Least Absolute Deviation Method of Curve Fitting

摘要:

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∑mi=1yi-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.

Abstract:

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.