The main result obtained in this paper is this:
If it is possible to do forward
modeling on a physical problem in a way that permits
the output (*i.e.*, the predicted values of some physical
parameter that could be measured) and the first derivative of
that same output with respect to model parameters
(whatever they may be) to be calculated numerically, then
(at least in principle) it is possible to solve the inverse
problem using the method described.
The main trick learned in this analysis comes from the realization
that the steps in the model updates may have to be quite
small in some cases for the implied guarantees of convergence to
be realized.

We have concentrated on least-squares methods in the presentation
in order to keep the analysis simple. However, it is clear that the
general method presented could be applied as well to any norm
of the data discrepancies that possesses the same necessary
qualities, the most important of these being the existence of a first
derivative with respect to the model parameters. One interesting
example of such an alternative is Huber's hybrid of *l _{1}* and

11/12/1997