[petsc-users] eigensolution error with slepc

[Jose E. Roman]

> 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.

Jose