On Jul 16, 2011, at 5:11 PM, Barry Smith wrote: > > Jed, > > I just remembered something I should have said when we talked about the > rewrite of the KSPSPECEST stuff. > > If one has the bound on the smallest eigenvalue of the (preconditioned) > operator then ones convergence test can take that into account and know that > the 2-norm of the error of the linear solver (as opposed to the 2 norm of the > residual) is less than some
Humm, the only linear algebra proof that I know gives bounds on the error of the form | error |_2 <= Condition-number * | residual |_2, for SPD matrices of course. This is pessimistic but I'm not sure how you could get a bound on error with only the lowest eigen value ... Mark > tolerance. Of course the KSPSPECEST can give us this information, even though > Mark doesn't believe it is accurate enough :-), with enough iterations it can > be. So ideally we'd have options that allowed convergence tests to use the > estimate of the error norm instead of just the residual norm. > > Barry > >
