[petsc-users] Question about rank of matrix

[Pierre Jolivet]

> On 17 Feb 2023, at 8:56 AM, Stefano Zampini <stefano.zampini at gmail.com> wrote:
> 
> 
> On Fri, Feb 17, 2023, 10:43 user_gong Kim <ksi2443 at gmail.com <mailto: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.
>> 
>> Thanks,
>> Hyung Kim
> 
> 
> My experience with this is usually associated to reading a book and find the solution I'm looking for. 

On top of that, some exact factorization packages can solve singular systems, unlike what you are stating.
E.g., MUMPS, together with the option -mat_mumps_icntl_24, see https://mumps-solver.org/doc/userguide_5.5.1.pdf

Thanks,
Pierre
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