Because the second derivative is not positive everywhere, the Cauchy function introduces the possibility of multiple solutions, but because of the good results we see in Figure , you might like to try it anyway. Perhaps the reason it seems to work so well is that it uses mostly residuals of ``average size,'' not the big ones or the small ones. This happens because is made from and the components of which are a function that is maximum for those residuals near .
Module irls supplies two useful weighting functions that can be interchanged as arguments to the reweighted scheme . irlsweighting functions for iterative reweighting