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 ∑i=1m|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.