A Hybrid Method For Nonlinear Least Squares That Uses Quasi-Newton Updates Applied To An Approximation Of The Jacobian Matrix

In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that A(T)f = J(T)f. This property allows us to solve a linear least squares problem, minimizing parallel to Ad + f parallel to instead of solving the normal equation A(T) Ad + J(T) f = 0, where d is an element of R-n is the required direction vector. Computational experiments confirm the efficiency of the new method.