[petsc-users] Questions on QR methods in PETSc

[Matthew Knepley]

Hi Leonardo,

On Fri, Mar 27, 2026 at 11:35 AM Leonardo De Novellis via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear Users Support Team,
> I have a couple of questions regarding QR decompositions in PETSc.
>
> 1) I would like to find the least-squares solution of a rectangular system
> of the form Ax = b, where A is a dense and tall-skinny matrix (size around
> 1000000 x 10).
> Since A has very bad conditioning, I want to avoid iterative methods (such
> as KSPLSQR), since the number of iterations can get very large, and would
> like to use a direct QR solving method.
> Currently, I am running my code on only 1 core, and A is of type seqaij.
> With this setup, the following code works fine:
>
> call KSPSetType(ksp, KSPPREONLY, ierr)
> call KSPGetPC(ksp, pc, ierr)
> call PCSetType(pc, PCQR, ierr)
> call KSPSetOperators(ksp, A, A, ierr)
> t1 = MPI_Wtime()
> call KSPSolve(ksp, b, x, ierr)
> t2 = MPI_Wtime()
>
> I eventually want to run this in parallel on multiple cores. Will PCQR
> work for an mpiaij / mpidense matrix?
>

No it is only serial. We could call the ScLAPACK or Elemental version of
QR, but we don't right now.


> If not, what would you suggest as a direct solving approach for this
> system?
>

It would be easy to make the normal equations (dot products would make the
matrix on all procs) and factor.


> 2) I would also like to compute an explicit QR decomposition of A, and
> want to do so in parallel. Is there any way to do so in PETSc? If not, as a
> possible alternative, would you recommend using SLEPc BVOrthogonalize
> function?
>

I would definitely recommend using BV. I have been meaning to pull that
into PETSc because it is so great, but have not done it yet. You can just
reconfigure with --download-slepc and run with it.

  Thanks,

     Matt


> Kind regards,
> Leonardo
>
>
>

-- 
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

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