Iteratively reweighted least squares

The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form:

by an iterative method in which each step involves solving a weighted least squares problem of the form:

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.