[petsc-dev] GMRES and eigen estimates

[Jed Brown]

On Tue, Apr 3, 2012 at 14:05, Barry Smith <bsmith at mcs.anl.gov> wrote:

> 2)  "I turn off norms for this -- its in the eigen estimate -- because I
> don't usually want them. "    But doesn't GMRES compute the norms always?
> So why not have the GMRES version still kick out early if the norm reduces
> by same 10^10 before it ran out of its? (Since the norm is "free" for GMRES
> there is no harm done, and good things occasionly like your case below.


Yeah, though this is an ideal scenario for TSQR-based GMRES in which case
we would have done several iterations with one reduction. You will still
have the norms, but I guess we will need to check them and decide which
estimates to use. So I guess no problem at this point, but something to
keep in mind with spectral estimates using TSQR-based or pipelined
(latency-tolerant) GMRES.

Mark, because CG runs in a norm that is stronger with respect to low
frequencies/weaker with respect to high frequencies, but we only want an
accurate estimate of the highest eigenvalue, I would expect GMRES to give
this estimate sooner. Do you not observe this?
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