1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 National Institute of Aquatic Resources, Technical University of Denmark4 Department of Applied Mathematics and Computer Science, Technical University of Denmark
We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES - their success as regularization methods is highly problem dependent.