[petsc-users] Solving tridiagonal hermitian generalized eigenvalue problem with SLEPC

[Jed Brown]

Toon Weyens <tweyens at fis.uc3m.es> writes:

> Hi, thanks for the answers!
>
> I think I expressed myself wrong: I can indeed get it to work with just
> using AIJ matrices, as in example 13. This is the way that I am currently
> solving my problem. There are only two issues:
> 1. memory is indeed important so I would certainly like to decrease it by
> one third if possible :-) The goal is to make the simulations as fast and
> light as possible to be able to perform parameter studies (on the stability
> of MHD configurations).

What do your matrices represent?  If A and B are really tridiagonal,
then memory needed for matrix storage is irrelevant because the Krylov
vectors will dominate.

> 2. I have played around a little bit with the different solvers but it
> appears that the standard method and the Arnoldi with explicit restart
> method are the best. Some of the others don't converge and some are slower.
>
> The thing is that in the end the matrices that I use are large but they
> have a very easy structure: hermitian tri-diagonal. That's why, I think,
> slepc usually converges in a few iterations (correct me if I'm wrong).
>
> The problem is that sometimes, when I consider more grid points, the solver
> doesn't work any more because apparently it uses the LU decomposition (not
> sure for the matrix A or B in A x = lambda B x) 

The factorization is for B because you are not using inversion (usually
to target interior eigenvalues or those near 0).  What is B?
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