Numerical errors resulting from the simulators discretization and integration
algorithms, coupled with finite differences errors in the evaluation of the
Jacobian could result in a poor convergence behavior of the
Levenberg-Marquardt algorithm in the proximity of the solution. The use of a
response surface quadratic approximation of the objective function near
its minimum is suggested as a possible remedy. The model could be built
using the task macromodeling existing capability. Indeed, It might be possible
to use the task module extension language to prototype and evaluate this
approach before the actual code development process is attempted.