Re: KKT constraint preconditioner

On Wed, 23 Apr 2008 06:31:08 -0700 (PDT), laverneth@xxxxxxxxx wrote:

I want to solve a full KKT system of the form
[A C ]
[CT 0 ]
with A is a n,n matrix, and C is a n,m matrix representing m
constraints on the n primal variables,
and CT is its transpose.

I am trying to solve this method with an iterative method (namely
BiCGSTAB), and thus I need a good preconditioner.
Often, the constraint precondionner is described in the litterature
and I tried to implement it.
It involves approximate solves with the m,m system CT *C. I tried to
use a SAINV factorization on that system which has the great advantage
to avoid forming the matrix CT*C explicitly (see 1) for reference).

However, in my case C has not full column rank and Ct*C is therefore
indefinite and SAINV factorization breaks down because of exactly zero
pivots. Has anyone an idea to avoid such zero pivots in the
factorization ? Should I use an other factorization ?

Why do you have linearly dependent constraints?
.

Relevant Pages

  • Re: KKT constraint preconditioner
    ... use a SAINV factorization on that system which has the great advantage ... Has anyone an idea to avoid such zero pivots in the ... Why do you have linearly dependent constraints? ... usual trick is to add artificial varaibles that are constrained to be ...
    (sci.math.num-analysis)
  • Re: KKT constraint preconditioner
    ... constraints on the n primal variables, ... use a SAINV factorization on that system which has the great advantage ... to avoid forming the matrix CT*C explicitly for reference). ... Why do you have linearly dependent constraints? ...
    (sci.math.num-analysis)
  • Re: KKT constraint preconditioner
    ... use a SAINV factorization on that system which has the great advantage ... to avoid forming the matrix CT*C explicitly for reference). ... Why do you have linearly dependent constraints? ... I have intersecting interfaces with constraints on dofs on each side ...
    (sci.math.num-analysis)
  • KKT constraint preconditioner
    ... I am trying to solve this method with an iterative method (namely ... use a SAINV factorization on that system which has the great advantage ... indefinite and SAINV factorization breaks down because of exactly zero ... Has anyone an idea to avoid such zero pivots in the ...
    (sci.math.num-analysis)
Loading