[petsc-users] Ambiguity of KSPCGNE

[Jed Brown]

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.
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