TWO-PARAMETER REGULARIZED GAUSS-NEWTON TYPE METHODS FOR HIGHLY NONLINEAR LEAST SQUARES PROBLEMS

This report treats numerical methods for highly nonlinear least squares problems for which procedural and rounding error are unavoidable, e.g. those arising in the development of various nonlinear system identification techniques based on input-output representation of the model such as training of ar- tificial neural networks. Let F be a Frechet-differentiable operator acting between Hilbert spaces 1 H and 2 H and such that the range of its first derivative is not necessarily closed. For solving the equation 0 ) ( = x F or minimizing the functional