Thanks Barry for the paper. I also noticed that the block lower preconditioner also has the same minimal polynomial (the proof is similar), hence left and right preconditioning shall apply the same.
Giang On Fri, Jun 23, 2017 at 9:14 PM, Barry Smith <[email protected]> wrote: > > Based on my reading of the attached paper, in particular the last line > on page 1050 I don't think it matters. > > and P−1A and AP−1 have the minimal polynomial (λ − 1)2. > > since the application on either side matches the same polynomial. > > > Barry > > > > > > On Jun 23, 2017, at 11:48 AM, Hoang Giang Bui <[email protected]> > wrote: > > > > Hello > > > > I just want to make sure that I understand the right thing, in the > manual page of PCFieldSplitSetSchurFactType: > http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/ > PCFieldSplitSetSchurFactType.html > > > > The "upper" option uses DU from the full factorization. If I understand > correctly, the ksp must be used with right preconditioning, because A P^-1 > = (LDU) * (DU)^(-1) = L. If that was the case, should the manual put this > information to be more clear? > > > > Thanks > > Giang > > > > >
