Petsc And Slepc, singular system

Matthew Knepley knepley at
Tue Jul 21 15:56:11 CDT 2009

On Tue, Jul 21, 2009 at 3:16 PM, Umut Tabak <u.tabak at> wrote:

> Dear all,
> As a fresh user of Petsc libraries, should thank the developers for such a
> magnificent endeavor and years of work.
> So the question directly related to Petsc is that if I have a singular
> system matrix and try to solve for the unknowns(simple enough 3 by 3) (I am
> using the simple linear system example from the Petsc user manual as a
> template where a preconditioner is used, I guess it is Jacobi.), I do not
> get any warnings for zero pivots in LU decomposition which I could not
> understand why, and the results are on the order of e+16, also the norm of
> the error. But why is not there some kind of warning.

If your system is badly scaled, roundoff errors could result in a pivot
larger than our tolerance. It is also possible that your preconditioner
resulted in a badly scaled system.


> The second part of the question is related to Slepc, this might not find
> direct answers here perhaps, but let me give it a try.
> I have a generalized eigenvalue problem, it is a vibration related problem
> so I will use K and M instead of A and B, respectively. On my problem, K is
> singular, and if I use slepc to find the solution, petsc warns me about the
> zero pivot emergence, and breaks down naturally, there after I apply some
> shift operations that are already implemented in slepc to overcome the
> problem.
> The question is what is the effect of preconditioner on a singular matrix
> for the linear system explained above, somehow, I was thinking in any case
> that should also warn me but it did not and gave some wrong results.
> I am a bit weak on the preconditioners, maybe should have done some reading
> but I know that singular systems can also have solutions by some order
> tricks, pseudo inverse, temporary links application solutions with respect
> to rigid body modes(from structural mechanics too specific maybe).
> Can Petsc handle singular systems as well? I am a bit confused at this
> point.
> Best regards,
> Umut

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