@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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