[petsc-users] Solving dense rectangular linear systems

[Jed Brown]

Rakesh Halder <rhalder at umich.edu> writes:

> Hi all,
>
> I'm wondering what the recommended method is to solve linear systems Ax=b,
> where A is an N by n matrix (N >> n) and dense. I've used the CGLS and LSQR
> algorithms, but have issues applying any kind of preconditioner. Looking at
> the PETSc documentation, it doesn't look like there are any direct solvers
> for rectangular systems, but only iterative ones which aren't very useful
> for dense systems.

QR is the standard technique. For a highly parallel implementation, I would check out BVOrthogonalize() from SLEPc, which has several good options. Arguably, this feature should be migrated to PETSc.  

> I'm also wondering if it's best to use a dense or sparse (AIJ) matrix
> format in general when working with dense matrices. I've just been using
> sparse matrices, due to being able to preallocate memory.
>
> Thanks,
>
> Rakesh Halder