[petsc-users] Question about rank of matrix

[Matthew Knepley]

On Fri, Feb 17, 2023 at 2:43 AM user_gong Kim <ksi2443 at gmail.com> wrote:

> Hello,
>
> I have a question about rank of matrix.
> At the problem
> Au = b,
>
> In my case, sometimes global matrix A is not full rank.
> In this case, the global matrix A is more likely to be singular, and if it
> becomes singular, the problem cannot be solved even in the case of the
> direct solver.
> I haven't solved the problem with an iterative solver yet, but I would
> like to ask someone who has experienced this kind of problem.
>
> 1. If it is not full rank, is there a numerical technique to solve it by
> catching rows and columns with empty ranks in advance?
>
> 2.If anyone has solved it in a different way than the above numerical
> analysis method, please tell me your experience.
>

As Pierre points out,  MUMPS can solve singular systems.

If you have an explicit characterization of the null space, then many
iterative methods can also solve it by projecting out
the null space. You call MatSetNullSpace() on the system matrix.

  Thanks,

     Matt


> Thanks,
> Hyung Kim
>
>
>

-- 
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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