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

[Xujun Zhao]

Does shell matrix work?

On Wed, Jun 3, 2015 at 11:04 AM, Xujun Zhao <xzhao99 at gmail.com> wrote:

> 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
>
> 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
>>
>>
>
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