  When a physical system is modeled by a nonlinear function, the unknown
parameters can be estimated by fitting experimental observations by a
least-squares approach. Newton's method and its variants are often used to
solve problems of this type. In this paper, we are concerned with the
computation of the minimal-norm solution of an underdetermined nonlinear
least-squares problem. We present a Gauss-Newton type method, which relies on
two relaxation parameters to ensure convergence, and which incorporates a
procedure to dynamically estimate the two parameters, as well as the rank of
the Jacobian matrix, along the iterations. Numerical results are presented.
