Solution of Robust Linear Regression Problems by Krylov Subspace Methods

Abstract

Several methods have been suggested for obtaining the estimates of the solution vector for the robust linear regression model Ax=b+ε using an iteratively reweighted criterion based on weighting functions, which tend to diminish the influence of outliers. We consider a combination of Newton method (or iteratively reweighted least squares method) with a Krylov subspace method. We show that we can avoid preconditioning with A ^T A preconditioner by merely transforming the sequence of linear systems to be solved. Appropriate sequences of linear systems for sparse and dense matrices are given. By employing efficient sparse QR factorization methods, we show that it is possible to solve efficiently large sparse linear systems with an unpreconditioned Krylov subspace method.