[petsc-users] estimation of max and min eigenvalues in SLEPc

[Jose E. Roman]

El 03/06/2015, a las 18:04, Xujun Zhao escribió:

> One problem is that I don't have the explicit form of matrix D, but only u = D*v which can be obtained from my PETSc solver. How should I set up my EPSSolver in this case? Are there examples in SLEPc? Thanks.
> 
> Xujun


http://slepc.upv.es/documentation/current/src/eps/examples/tutorials/ex3.c.html
http://slepc.upv.es/documentation/current/src/eps/examples/tutorials/ex6f.F.html


> 
> On Wed, Jun 3, 2015 at 10:59 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:
> 
> El 03/06/2015, a las 17:47, Xujun Zhao escribió:
> 
> > Hi Jose,
> >
> > Thank you for your reply. How about the computational cost compared to one EPSSolve() with all eigenvalues? what methods does SLEPc use for each solve? Because it may be cheaper for largest eigenvalue if the power method is used, but I don't if it is still so for smallest eigenvalue?
> >
> > Xujun
> >
> 
> Don't compute all eigenvalues.
> 
> For the largest eigenvalue, don't use the power iteration. The default solver (Krylov-Schur) will be very fast for that. For the smallest eigenvalue, convergence may be slow if eigenvalues are small and poorly separated - it may be necessary to do shift-and-invert, in which case the cost may blow up.
> 
> Jose
> 
>