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Re: minpack code for least squares?
From: |
Jaroslav Hajek |
Subject: |
Re: minpack code for least squares? |
Date: |
Fri, 15 Feb 2008 10:28:14 +0100 |
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