[petsc-dev] KSP convergence test based on error on residual

[Mark F. Adams]

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
> 
>