Inner-Iteration Krylov Subspace Methods for Least Squares Problems

Stationary inner iterations in combination with Krylov subspace methods are proposed for overdetermined least squares problems. The inner iterations are efficient in terms of computational work and memory and also serve as powerful preconditioners for ill-conditioned and rank-deficient problems. Theoretical justifications for using the inner iterations as preconditioners are presented. Numerical experiments on overdetermined sparse least squares problems show that the proposed methods outperform previous methods, especially for ill-conditioned and rank-deficient problems.