Hi Leonardo, On Fri, Mar 27, 2026 at 11:35 AM Leonardo De Novellis via petsc-users < [email protected]> 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
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