# [petsc-users] How to compute the condition number of SchurComplementMat preconditioned with PCSHELL.

Wed Nov 10 08:09:35 CST 2021

Great thanks, Matt!

The second option is what I was looking for.

Best Regards,

________________________________
От: Matthew Knepley <knepley at gmail.com>
Отправлено: 10 ноября 2021 г. 16:45:00
Копия: petsc-users at mcs.anl.gov
Тема: Re: [petsc-users] How to compute the condition number of SchurComplementMat preconditioned with PCSHELL.

Dear PETSc community,

I wonder if you could give me a hint on how to compute the condition number of a preconditioned matrix in a proper way.

I have a MatSchurComplement matrix S and a preconditioner P of the type PCSHELL (P is a diffusion matrix, which itself is inverted by KSPCG).

I tried to compute the condition number of P^{-1}S "for free" during the outer PCG procedure using KSPComputeExtremeSingularValues() routine.

Unfortunately, \sigma_min does not converge even if the solution is computed with very high precision.

I also looked at SLEPc interface, but did not realised how PC should be included.

You can do this at least two ways:

1) Make a MatShell for P^{-1} S. This is easy, but you will not be able to use any factorization-type PC on that matrix.

2) Solve instead the generalized EVP, S x = \lambda P x. Since you already have P^{-1}, this should work well.

Thanks,

Matt

Thanks!

Sincerely,

--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
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