Re: Overdetermined, non-linear

["Matthew Knepley" <knepley@xxxxxxxxx>]

On Feb 1, 2008 5:54 AM, Erlend Pedersen :.
<erlend.pedersen@xxxxxxxxxxxxx> wrote:
> I am attempting to use the PETSc nonlinear solver on an overdetermined
> system of non-linear equations. Hence, the Jacobian is not square, and
> so far we have unfortunately not succeeded with any combination of snes,
> ksp and pc.
>
> Could you confirm that snes actually works for overdetermined systems,
> and if so, is there an application example we could look at in order to
> make sure there is nothing wrong with our test-setup?
>
> We have previously used the MINPACK routine LMDER very successfully, but
> for our current problem sizes we rely on the use of sparse matrix
> representations and parallel architectures. PETSc's abstractions and
> automatic MPI makes this system very attractive for us, and we have
> already used the PETSc LSQR solver with great success.

So in the sense that SNES is really just an iteration with an embedded solve,
yes it can solve non-square nonlinear systems. However, the user has to
understand what is meant by the Function and Jacobian evaluation methods.
I suggest implementing the simplest algorithm for non-square systems:

http://en.wikipedia.org/wiki/Gauss-Newton_algorithm

By implement, I mean your Function and Jacobian methods should return the
correct terms. I believe the reason you have not seen convergence is that
the result of the solve does not "mean" the correct thing for the iteration
in your current setup.

   Matt

> Thank you very much.
>
>
> Regards,
> Erlend Pedersen :.
-- 
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