# [R] nls.lm

ProfJCNash profjcnash at gmail.com
Wed Oct 19 14:56:35 CEST 2016

Peter is right that the conditions may be embedded in the underlying code. (Ask Kate!)

My nlmrt package is all in R, so the conditions are visible. I'm currently in process of rejigging this
using some work Duncan Murdoch helped with a while ago (I've had some other things get in the way), so
I can change such conditions. In the present case, I think I'd issue a warning, but haven't checked
whether I do or not.

I'd be very happy to have the usual "minimal reproducible example" scripts of issues with any nonlinear
least squares problems to use as tests to keep knocking the rough edges off the codes I'm working on.
Note, in particular, that the new code (named nlsr) tries to use analytic derivatives that are computed
from the model expression. Ultimately would like to have automatic derivatives to apply to functions too,
and migrate that to optimrx/optimr which are recently on Rforge/CRAN (optimr has fewer solvers to avoid
the "your program doesn't work" when a solver is changed/removed).

Best, JN

On 16-10-19 08:09 AM, Mike meyer wrote:
> @pd: you know that a System of equations with more variables than equations is always solvable
> and if a unique solution is desired one of mimimal norm can be used.
>
> According to "Methods for nonlinear least squares problems" by Madsen, Nielsen and Tingleff the LM-algorithm
> solves Systems of the form
>                             [J(x)'J(x)+\mu*I]x=...
> with \mu>0 so that the Matrix on the left is always positive definite, especially nonsingular.
>
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