Re: minpack code for least squares?

[Jaroslav Hajek]

On Fri, Feb 15, 2008 at 7:35 AM, Olaf Till <address@hidden> wrote:
> > Further, MINPACK's LMDER and LMDIF are likely the most widely used
>  > nonlinear least-squares codes in history, so they're sort of "proven
>  > quality".
>
>  'leasqr' (m-code, in 'optim') also provides an l/m-algorithm,
>  optionally with user-supplied jacobian.

After quickscan it seems that leasqr relies on SVD factorization of
the jacobian,
while MINPACK uses pivoted QR (faster). Also, MINPACK features
a trust-region subproblem to select the actual step, whereas
leasqr seems to use some heuristics to select the l/m parameter in
successive steps. Trust-region techniques have the reputation to improve
global convergence [see e.g. Nocedal]

>  Seems to work well, we had
>  problems in which it did converge, though Matlabs 'lsqcurvefit'
>  l/m-method only pretended to and lingered at the starting values. It
>  should be tested carefully if 'lmder' and 'lmdif' are indeed
>  better. Even in this case I would vote to have the 'leasqr' code kept
>  in place.
>

no question; even if MINPACK gave better fit in all cases (which is
rarely seen),
there are other useful options and output statistics in leasqr that
are not found
in MINPACK.


>  Olaf
>

regards

-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz