In recent years there have been a variety of methods proposed
for solving general nonlinear DAEs. Several of these methods
require repeatedly solving a nonlinear least squares problem
for a solution that is not unique. While the methods theoretically
only require the unique part of the solution, it has been seen
that the nonunique parts can pose numerical difficulties or put
restrictions on how the integrator is implemented. In this paper
we examine a modification of the classical Gauß-Newton iteration
which is designed to control the size of the terms that are not unique.

We will first develop the iteration scheme and analyze its convergence
properties. We will then illustrate its application to the integration
of differential algebraic equations.