On the Properties of Preconditioners for Robust Linear Regression
Venansius Baryamureeba and Trond Steihaug
Reports in Informatics No. 184, March 2000, Department of
Informatics, University of Bergen, Norway.
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.