[petsc-users] eigensolution error with slepc

David Knezevic david.knezevic at akselos.com
Mon Apr 4 12:29:53 CDT 2016

On Mon, Apr 4, 2016 at 1:27 PM, Jose E. Roman <jroman at dsic.upv.es> wrote:

> > El 4 abr 2016, a las 19:13, David Knezevic <david.knezevic at akselos.com>
> escribió:
> >
> > 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
> In terms of linear algebra, a symmetric-indefinite matrix pencil is not
> symmetric (no guarantee it has real eigenvalues and a full set of linearly
> independent eigenvectors). So in principle a non-symmetric algorithm should
> be used. The GHIEP solver tries to enforce (pseudo-) symmetry throughout
> the computation. This may provide more accurate results or maybe converge
> faster, but the cost per iteration is higher (since it uses B-inner
> products rather than standard inner products as in Arnoldi). Maybe in
> problems arising in buckling analysis of structures it is always safe to
> use GHIEP, I don't know.

OK, got it, thanks!

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