Preconditioners for rank deficient least squares problems

Abstract

In this paper we present a method for computing sparse preconditioners for iteratively solving rank deficient least squares problems (LS) by the LSMR method. The main idea of the method proposed is to update an incomplete factorization computed for a regularized problem to recover the solution of the original one. The numerical experiments for a wide set of matrices arising from different science and engineering applications show that the preconditioner proposed, in most cases, can be successfully applied to accelerate the convergence of the iterative Krylov subspace method.