An algorithm for solving sparse nonlinear least squares problems (Q1822462)

We introduce a new method for solving nonlinear least squares problems when the Jacobian matrix of the system is large and sparse. The main features of the new method are the following: a) The Gauss-Newton equation is ''partially'' solved at each iteration using a preconditioned conjugate gradient algorithm. b) The new point is obtained using a two- dimensional trust region scheme, similar to the one introduced by Bulteau and Vial. We prove global and local convergence results and we present some numerical experiments.