# [R] nls.lm

Berend Hasselman bhh at xs4all.nl
Wed Oct 19 17:28:07 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.
>

Not true.

Take the system with 3 variables and 2 equations

x+y+z = 3
x+y+z = 4

This does not have a solution.
See https://en.wikipedia.org/wiki/Consistent_and_inconsistent_equations

Berend

> 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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