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

Jed Brown jedbrown at mcs.anl.gov
Sat Jul 16 16:17:43 CDT 2011

On Sat, Jul 16, 2011 at 16:11, Barry Smith <bsmith at mcs.anl.gov> 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 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.

I would expect it to become a good approximation when the KSP has converged
on the low-frequency modes. I think Mark's objection is that a few
iterations are usually nowhere near actually converging, so you can only use
the estimate in a meaningful way to estimate the high end of the spectrum.

> So ideally we'd have options that allowed convergence tests to use the
> estimate of the error norm instead of just the residual norm.

How would you suggest handling restarts?
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