docs for MINRES, only for positive definite?

[Matthew Knepley]

On Thu, Feb 28, 2008 at 11:35 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>    symmetry has nothing to do with it. Yes the matrix and
>  preconditioner must be
>  symmetric. The point is that the preconditioner has to also be
>  positive definite.
>  Because B is used in the algorithm to define a norm.

I disagree. Here is a weaker condition:

  1) A is symmetric indefinite and so is B

  2) BA is also symmetric

Since A and B are full rank, so is BA. Thus BA is symmetric indefinite
and MINRES will work.
My comment was that if B is SPD, then BA is equivalent to B^1/2 A
B^1/2 and thus symmetric.

   Matt

>     Barry
>
>
>
>  On Feb 28, 2008, at 11:28 AM, Matthew Knepley wrote:
>
>  > On Thu, Feb 28, 2008 at 11:25 AM, Lisandro Dalcin
>  > <dalcinl at gmail.com> wrote:
>  >> Good point, the current code seems to require that...
>  >
>  > Its not the code, its the algorithm. It requires symmetry.
>  >
>  >  Matt
>  >
>  >>  ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /*     z  <- B*r       */
>  >>  ierr = VecDot(R,Z,&dp);CHKERRQ(ierr);
>  >>  /*...*/
>  >>  if (dp < 0.0) {
>  >>    ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
>  >>    PetscFunctionReturn(0);
>  >>  }
>  >>
>  >> Indeed, the following (simple minded, diagonal matrix) test fails
>  >> with
>  >> -pc_type jacobi, but success with -pc_type none
>  >>
>  >> import sys, petsc4py
>  >> petsc4py.init(sys.argv)
>  >> from petsc4py import PETSc
>  >> import numpy as N
>  >> A = PETSc.Mat().createAIJ([10,10])
>  >> for i in range(0,5):
>  >>    A[i,i] = -(i + 1)
>  >> for i in range(5,10):
>  >>    A[i,i] = +(i + 1)
>  >> A.assemble()
>  >> A.view()
>  >> x, b= A.getVecs()
>  >> b.set(1)
>  >> ksp = PETSc.KSP().create()
>  >> ksp.type = 'minres'
>  >> ksp.setOperators(A)
>  >> ksp.setFromOptions()
>  >> ksp.solve(b,x)
>  >>
>  >>
>  >>
>  >>
>  >> On 2/28/08, Barry Smith <bsmith at mcs.anl.gov> wrote:
>  >>>
>  >>>    But does it require a positive definite preconditioner?
>  >>>
>  >>>
>  >>
>  >>
>  >>>    Barry
>  >>>
>  >>>
>  >>> On Feb 28, 2008, at 9:32 AM, Matthew Knepley wrote:
>  >>>
>  >>>> Docs are wrong.
>  >>>>
>  >>>> Matt
>  >>>>
>  >>>> 2008/2/28 Lisandro Dalcin <dalcinl at gmail.com>:
>  >>>>> I've noticed that the docs for MINRES say that the operator and
>  >>>>> the
>  >>>>> preconditioner must be POSITIVE DEFINITE. But I understand
>  >>>>> MINRES is
>  >>>>> tailored for the symmetric/hermitian-indefinite case.
>  >>>>>
>  >>>>> Are the docs wrong? Or the actual code is a (very peculiar) MINRES
>  >>>>> variant?
>  >>>>>
>  >>>>>
>  >>>>> --
>  >>>>> Lisandro Dalcín
>  >>>>> ---------------
>  >>>>> Centro Internacional de Métodos Computacionales en Ingeniería
>  >>>>> (CIMEC)
>  >>>>> Instituto de Desarrollo Tecnológico para la Industria Química
>  >>>>> (INTEC)
>  >>>>> Consejo Nacional de Investigaciones Científicas y Técnicas
>  >>>>> (CONICET)
>  >>>>> PTLC - Güemes 3450, (3000) Santa Fe, Argentina
>  >>>>> Tel/Fax: +54-(0)342-451.1594
>  >>>>>
>  >>>>>
>  >>>>
>  >>>>
>  >>>>
>  >>>> --
>  >>>> What most experimenters take for granted before they begin their
>  >>>> experiments is infinitely more interesting than any results to
>  >>>> which
>  >>>> their experiments lead.
>  >>>> -- Norbert Wiener
>  >>>>
>  >>>
>  >>>
>  >>
>  >>
>  >> --
>  >> Lisandro Dalcín
>  >> ---------------
>  >> Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
>  >> Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
>  >> Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
>  >> PTLC - Güemes 3450, (3000) Santa Fe, Argentina
>  >> Tel/Fax: +54-(0)342-451.1594
>  >>
>  >>
>  >
>  >
>  >
>  > --
>  > What most experimenters take for granted before they begin their
>  > experiments is infinitely more interesting than any results to which
>  > their experiments lead.
>  > -- Norbert Wiener
>  >
>
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener