Re: [Help-gsl] Sparse Levenberg-Marquardt

[Brian Gough]

At Mon, 14 Sep 2009 13:46:52 +0000,
Tom Banwell wrote:
> I was wondering if you could help me.  I have a nonlinear least
> squares problem that has a large number of parameters, greater than
> 1,000.  I am currently solving it using the current version of GSL,
> Levenberg-Marquardt algorithm.  This works well but it is slow and
> takes several seconds.  I would ideally like it to be a lot less time,
> and have read that I can exploit the spareness of the jacobians using
> QR factorization.  Most of my parameters are not dependent on other
> parameters and my jacobian is therefore quite sparse.

Hello,

Thanks for your email.  We use the Householder method for QR
decomposition.  As I understand it, the Given's method is better for
sparse matrices and Householder is better in the general case.  The two
methods are compared in Golub and van Loan's "Matrix Computations"
chapter on QR.  We only support dense matrices in GSL, but I think even
without a sparse matrix representation Given's would be an advantage.

It would be good to provide a version of the LM routines for Given's but
nobody is working on that.  If you would like to volunteer to try it
would be very useful.

-- 
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/