> On 6 Jul 2018, at 17:30, zakaryah <[email protected]> wrote: > > Thanks for your help, Barry. > > I agree about the preconditioning. I still don't understand why I don't need > a particular solver for my shell matrix. My reasoning is that KSP is easy > with M but difficult with A, since A has a dense row and column, whereas M is > entirely sparse. Sherman-Morrison seems to be an efficient way of dealing > with this but I could be wrong.
As Barry says, low-rank perturbations are not terrible for the convergence of Krylov methods. E.g. Theorem 2.1 of https://arxiv.org/pdf/1508.07633.pdf and a refinement in https://arxiv.org/pdf/1612.08369.pdf with improved bounds. Cheers, Lawrence
