On Fri, Jul 6, 2018 at 11:44 AM Lawrence Mitchell < [email protected]> wrote:
> > > 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 While I agree with you guys that Krylov methods will probably work fine, my understanding of Strakos' results are that theorems of this kind crumble under rounding error perturbations. Maybe Patrick has a rejoinder for this. Thanks, Matt > > and a refinement in https://arxiv.org/pdf/1612.08369.pdf with improved > bounds. > > Cheers, > > Lawrence -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
