[petsc-users] Preconditioners for rectangular matrices

[Barry Smith]

  Rakesh,

   LSQR takes a square matrix from which to build a preconditioner.  When you call KSPSetOperators( ...   Rectangular, Square...) where Square is generally Rectangular transpose  * Rectangular.  LSQR essentially solves the normal equations so it makes sense to use for a preconditioner the normal equations matrix. Note that Square is a small matrix compared to Rectangular.

   You can use with this KSP now any preconditioner which is applied to the Square matrix, -pc_type lu, jacobi, gamg, ... 

  Barry


> On Nov 1, 2020, at 10:20 PM, Rakesh Halder <rhalder at umich.edu> wrote:
> 
> Hi all,
> 
> I'm implementing an algorithm using PETSc that involves solving a linear system Ax=b where A is a rectangular (non-square) matrix. I'm currently using KSP to solve this system using the CGLS method, but want to improve the performance. I've tried using a direct solver (PCLU with KSPPREONLY), but this seems to only work for square matrices. I'm wondering what methods are available in PETSc for preconditioning rectangular matrices so they can be solved directly through some factorization or with an iterative method like LSQR.
> 
> Thanks,
> 
> Rakesh