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Re: docs for MINRES, only for positive definite?


On Feb 28, 2008, at 11:44 AM, Matthew Knepley wrote:

On Thu, Feb 28, 2008 at 11:35 AM, Barry Smith <bsmith@xxxxxxxxxxx> 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.


But that is a different algorithm. That is running minres on the operator
BA with the preconditioner I which is very different than running
minres on A with the preconditioner B.



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@xxxxxxxxx> 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@xxxxxxxxxxx> 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@xxxxxxxxx>: 
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