We investigate the application of minimal residual and orthogonal residualsubspace correction methods to singular linear systems Ax = b. Special em-phasis is put on the special case of Krylov subspace methods. If A has index 1(i.e., if all Jordan blocks associated with the eigenvalue λ = 0 of A are 1× 1)the behaviour of these iterative methods is well understood (see, e.g., ...
