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Re: curve fitting: works badly?

I just peeked in here and saw a discussion of one of my recent
favorite topics, nonlinear least squares.  (We have IDL, but
I haven't learned it yet;  my brain is full :-) ).

I've been using the routine variously known as NL2SOL or N2G.  It is
described in ACM Trans. Math. Software, Vol. 9, PP. 369-383 (An
Adaptive Nonlinear Least-Squares Algorithm, By J.E. Dennis, D.M. Gay,
and R.E. Welsch).  They are available by anonymous FTP from
netlib.att.com in the freely distributable subset of the AT&T PORT
library.  It comes in several versions, including one which can bound
the fit parameters and versions which calculate the derivatives
numerically.  The precise details of the algorithm escape me at the
moment, but I'm using it to fit an 11-parameter (!) model to some
solar data.  Highly recommended.

As to errors: a recent article in Computers in Physics compared a
couple of different techniques for estimating the errors in a fit, and
concluded that Monte Carlo techniques give the best estimate.
Stephen Walton, California State University, Northridge
"Be careful what you wish for;  you might get it."	swalton@csun.edu