Stationary inner iterations in combination with Krylov subspace methods are proposed for least squares problems. The inner iterations are efficient in terms of computational work and memory, and serve as powerful preconditioners also for ill-conditioned and rank-deficient least squares problems. Theoretical justifications for using the inner iterations as preconditioners are presented. Numerical experiments for overdetermined least squares problems including ill-conditioned and rank-deficient problems show that the proposed methods outperform previous methods.
Morikuni et al. (Mon,) studied this question.