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

[Jed Brown]

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

> Yes, you are probably right: My code is not yet bug free (by all means!).
> However, I have been working very hard on it and I will see if I find
> something. B should not ever be really singular!
>
> I do, however, still have some questions:
>
> - Does slepc detect whether my matrix is tridiagonal and does it apply a
> direct method to solve it? Or do you talk about it in general: that it
> would be better for me to use a direct method that is not part of slepc?

The direct method is just a default.  For a tridiagonal matrix, there is
no fill, so direct methods have great complexity.  For other problems
(multi-dimensional, etc.) the direct solver has fill and becomes
asymptotically suboptimal.

> - How do I make use of the information that both A and B have the same
> non-zero structure? Is there an easy way?

I don't think it could make any difference for your scenario.

> - What is the call "MatSetOption(mat,MAT_HERMITIAN,PETSC_TRUE,ierr)" do? Is
> it important? It does not seem to influence anything...

In some circumstances, it would cause a method to default to Lanczos
instead of Arnoldi, or Cholesky instead of LU.
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