In this paper, we consider solving the robust linear regression problem, y = Ax+ ε 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 A ...

Numerical solution of linear least-squares problems is a key computational task in science and engineering. Effective algorithms have been developed for the linear least-squares problems in which the underlying matrices have full rank and are well-conditioned. However, there are few efficient and robust approaches to solving the linear least-squares problems in which the underlying matrices are...