[petsc-users] Ambiguity of KSPCGNE

[Barry Smith]

On Jun 22, 2012, at 4:11 PM, Jed Brown wrote:

> On Fri, Jun 22, 2012 at 9:19 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>  CGNE is only for people who have A (which is square) and want to solve the normal equations with CG using the preconditioner of A and its transpose for the preconditioner. Basically it allows the user to avoid computing A'A explicitly or making their own shell matrix.  It is definitely not a substitute for LSQR.
> 
> What? Maybe you are saying the same thing, but CGNE is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than eigenvalues. A unitary matrix is a classic example where CGNE converges in one iteration (unpreconditioned), but GMRES and CGS need N iterations.

   Maybe you should add this to the KSPCGNE manual page. Without the "What?" :-)

   Barry