  A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear
unconstrained optimization problems based on minimization of the sum squared
errors of the objective function residuals. Main advantage of the algorithm is
that it approximates matrix of q-second order derivatives with the first-order
q-Jacobian matrix. For that reason, the algorithm is much faster than
q-steepest descent algorithms. The convergence of q-GN method is assured only
when the initial guess is close enough to the solution. In this paper the
influence of the parameter q to the non-linear problem solving is presented
through three examples. The results show that the q-GD algorithm finds an
optimal solution and speeds up the iterative procedure.

Optimization and Control;Computational Complexity