Least Absolute Deviation Method of Curve Fitting

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.