Great to hear that the interface for slepc-3.0.0 is being upgraded. I
am another one of the users currently interfacing to slepc through
libmesh, although not entirely through libmesh classes. And so, I am
very interested in the coupling between these codes.

Anyway, I was curious about this statement by Jose:

> The Krylov-Schur method is mathematically equivalent to implicitly restarted
> Arnoldi, the method of Arpack, so there is currently no point in using SLEPc
> with Arpack.

I have noticed in my past experience that for many problems, they
basically required the same number of operator applications but IRAM
(from arpack) is far superior when the dominance ratio of the linear
system becomes closer to 1. So they might be mathematically equivalent
in some limit but I do not think it is fair to go far enough to say
that KrylovSchur=IRAM. My 2 cents.

PS: I would love to be proved wrong though because I have not looked
in to the math of this but am talking purely based on my experiments.

On Mon, Mar 23, 2009 at 4:17 PM, John Peterson <jwpeter...@gmail.com> wrote:
> On Mon, Mar 23, 2009 at 3:57 PM, Jose E. Roman <jro...@dsic.upv.es> wrote:
>>
>> On 23/03/2009, John Peterson wrote:
>>
>>> On Mon, Mar 23, 2009 at 2:08 PM, Kirk, Benjamin (JSC-EG311)
>>> <benjamin.kir...@nasa.gov> wrote:
>>>>
>>>> John - since you have at least used SLEPc, would  you please give this
>>>> patch
>>>> a look?  I think it is great that they did this for us!!
>>>
>>> The patch is now checked in.  At the moment I could only easily test
>>> against Petsc/Slepc 2.3.1, but whenever I get around to installing
>>> Petsc 3.0.0 I will take a look at this again.  I had to make a few
>>> changes to allow backwards-compatibility since EPSKRYLOVSCHUR was not
>>> yet available in Slepc 2.3.1.  Since I don't know when exactly it
>>> showed up, you now only get the Krylov-Schur solver when Petsc/Slepc
>>> 3.0.0 is available, otherwise you get ARNOLDI, which was the old
>>> default behavior.
>>>
>>> Perhaps the slepc developers could suggest a different or better
>>> default for versions of slepc prior to the introduction of
>>> Krylov-Schur?
>>
>> The Krylov-Schur solver was introduced in SLEPc 2.3.2, see
>> http://www.grycap.upv.es/slepc/download/changes.htm
>
> Alright, I updated the slepc_eigen_solver.C to only set KRYLOVSCHUR
> when SLEPc >= 2.3.2.  Thanks for pointing out the changes page, I
> should have found that myself :-/
>
>> I would suggest to set EPSKRYLOVSCHUR whenever it is available. An
>> alternative is to let SLEPc set the default solver.
>
> OK, examples 16 and 17 no longer try to set the eigensolver, although
> they show the user how it can be done (commented out).
>
>> The Krylov-Schur method is mathematically equivalent to implicitly restarted
>> Arnoldi, the method of Arpack, so there is currently no point in using SLEPc
>> with Arpack.
>
> Good to know!
>
> --
> John
>
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