  In these notes we propose and analyze an inertial type method for obtaining
stable approximate solutions to nonlinear ill-posed operator equations. The
method is based on the Levenberg-Marquardt (LM) iteration. The main obtained
results are: monotonicity and convergence for exact data, stability and
semi-convergence for noisy data. Regarding numerical experiments we consider:
i) a parameter identification problem in elliptic PDEs, ii) a parameter
identification problem in machine learning; the computational efficiency of the
proposed method is compared with canonical implementations of the LM method.
