On Large Scale Nonlinear Least Squares Calculations

The nonlinear model fitting problem is analyzed in this paper, with special emphasis on the practical solution techniques when the number of parameters in the model is large. Classical approaches to small dimensional least squares calculations are reviewed and an extension of them to problems involving many variables is proposed. This extension uses the context of partially separable structures, which has already proved its applicability for large scale optimization. An adaptable algorithm is discussed, which chooses between various possible models of the objective function. Preliminary numerical experience is also presented, which shows that actual numerical solution of a large class of fitting problems involving several hundreds of nonlinear parameters is possible at a reasonable cost.