[petsc-users] eigensolution error with slepc

[David Knezevic]

On Mon, Apr 4, 2016 at 12:47 PM, Jose E. Roman <jroman at dsic.upv.es> wrote:

>
> > El 4 abr 2016, a las 18:32, David Knezevic <david.knezevic at akselos.com>
> escribió:
> >
> > Hi Jose,
> >
> > I'm interested to know more about this comment from your email below:
> > "You can also try the symmetric-indefinite solver, but this is not
> recommended since it is not numerically stable."
> >
> > I frequently use SLEPc's symmetric-indefinite solver for buckling
> eigenvalue problems (which are naturally symmetric and indefinite), and
> this works well in my experience. But, based on your comment, I was
> wondering if you would recommend a different solver for this case?
> >
> > Thanks,
> > David
>
> The symmetric-indefinite solver is based on non-symmetric Lanczos, which
> is not guaranteed to be numerically stable (it does not rely on orthogonal
> projections as Arnoldi). In practice, it means that the method may break
> down or get unstable (in our implementation we detect the latter). For many
> problems the indefinite solver will provide the solution without problems,
> but no guarantees it will always work.
>
> Details of the indefinite solver can be found in section 3 of this paper:
> http://dx.doi.org/10.1007/s10543-016-0601-5
>
> Jose
>
>
OK, thanks, I'll have a look at that paper.

And just to confirm that I've understood properly: You're saying that the
GNHEP solver should converge more robustly than the GHIEP solver for
symmetric indefinite problems? Are there any advantages to using GHIEP over
GNHEP (e.g. is it faster?), or do you just recommend to always use GNHEP
for symmetric indefinite problems?

Apologies if the paper already answers those questions, I'll read through
it soon.

Thanks,
David
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