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 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
