IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set. For example, by minimizing the least absolute error rather than the least square error. Although not a linear regression problem, Weiszfeld’s algorithm for approximating the geometric median can also be viewed as a special case of iteratively reweighted least squares, in which the objective function is the sum of distances of the estimator from the samples. One of the advantages of IRLS over linear programming and convex programming is that it can be used with Gauss-Newton and Levenberg-Marquardt numerical algorithms. … Iteratively Reweighted Least Squares (IRLS) google