[petsc-users] Ambiguity of KSPCGNE

[Jed Brown]

http://petsc.cs.iit.edu/petsc/petsc-dev/rev/90ce2a6ecab0

On Fri, Jun 22, 2012 at 1:45 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> 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
>
>
>
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