El 27 mar 2026, a las 15:10, Leonardo De Novellis via petsc-users <[email protected]> escribió:

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

As an alternative, you can try PCSVD. If your matrix is ill-conditioned, I would trust SVD more than QR. Both PCQR and PCSVD are sequential, but PCSVD will work in parallel by creating a redundant dense matrix replicated in all processes, so that computation is still sequential. You can obtain a similar behaviour with PCREDUNDANT + PCQR.

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?

PETSc does not have parallel QR. In SLEPc BVOrthogonalize() will do the job. I would try the TSQR and SVQB methods, they should work for ill-conditioned matrices. With 1 MPI process TSQR should be equivalent to PCQR. You can also use the result of BVOrthogonalize() to compute the least-squares solution as x=R^{-1}*Q^T*b. Jose

Kind regards, Leonardo