# Overdetermined, non-linear

Erlend Pedersen :. erlend.pedersen at holberger.com
Tue Feb 5 03:26:56 CST 2008

```On Sun, 2008-02-03 at 19:59 -0600, Matthew Knepley wrote:
> On Feb 1, 2008 5:54 AM, Erlend Pedersen :.
> <erlend.pedersen at holberger.com> 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
>
>    Matt

Thanks. Good to know that I should be able to get a working setup. Are
there by any chance any code examples that I could use to clue myself in
on how to transform my m equations of n unknonwns into a correct
function for the Gauss-Newton algorithm?

- Erlend :.

```