On the Properties of Preconditioners for Robust Linear Regression

Abstract

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