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