  We consider large-scale nonlinear least squares problems with sparse
residuals, each of them depending on a small number of variables. A decoupling
procedure which results in a splitting of the original problems into a sequence
of independent problems of smaller sizes is proposed and analysed. The smaller
size problems are modified in a way that offsets the error made by disregarding
dependencies that allow us to split the original problem. The resulting method
is a modification of the Levenberg-Marquardt method with smaller computational
costs. Global convergence is proved as well as local linear convergence under
suitable assumptions on sparsity. The method is tested on the network
localization simulated problems with up to one million variables and its
efficiency is demonstrated.
