Error functions in curve fitting regression problem.

I want to perform a curve fitting regression analysis by using absolute deviation (S=sum{i=1 to n}|y(i)-f(x(i)|,where y(i) is the target value and f(x(i)) is the predicted value ) as the error function. It seems polyfit is used for polynomial regression analysis but it predicts the coefficients in least square sense. Are there any other inbuilt functions that I can use to solve my problem. Plz help me ,I am new to matlab.

Answer 1

[Torsten]

Approximation in l1 norm results in a linear optimization problem:

   min: sum_{i=1}^{n} eps_i

   s.c.

   y_i - f(x_i) <= eps_i
   y_i - f(x_i) >= -eps_i

   (i=1,...,n)

Unknowns are the eps_i and the polynomial coefficients.

Use linprog to solve.

Best wishes

Torsten.