# [R] nls.lm

Berend Hasselman bhh at xs4all.nl
Wed Oct 19 15:38:59 CEST 2016

> On 19 Oct 2016, at 14:09, Mike meyer <1101011 at gmx.net> 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.
>

You won't get  a minimum norm solution by using a least squares algorithm on the residuals.

> 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.
>

(from 2004; correct?).

In the first chapter at the very beginning it is clearly stated that the number of residuals (m) must be larger or equal to the number of independent variables (n).

And if m < n you have an underdetermined system of equations. You can't let a least squares method loose on that.
There is an infinity of solutions. You will first have to set the kind of solution you want: a minimum norm solution or something else.

I believe you are mistaken in your assertion.

Berend