Solutions of large-scale nonlinear systems VIA using quasi-Newton methods of order 1 and 2

This thesis studies numerical solutions of large-scale nonlinear systems using unconstrained optimization techniques. We focus on Quasi-Newton methods of order 1 and 2. We describe the methods, the corresponding algorithms, and their costs and convergence rates in order to allow a motivated methods choice. We limit ourselves to nonlinear linear systems resulting from finite elements discretization of boundary value problems.