Properties of Preconditioners for Robust Linear Regression

In this paper, we consider solving the robust linear regression problem y = Ax + ∈ by an inexact Newton method and an iteratively reweighted least squares method. We show that each of these methods can be combined with the preconditioned conjugate gradient least square algorithm to solve large, sparse systems of linear equations efficiently. We consider the constant preconditioner ATA and preconditioners based on low-rank updates and downdates of existing matrix factorizations. Numerical results are given to demonstrate the effectiveness of these preconditioners.