Convergence of Fixed Point Methods

This lecture covers the convergence of fixed point methods, discussing the global convergence property and uniqueness proofs. It explores the application of fixed point iterations and the consequences of Bolzano's theorem. The instructor presents the convergence criteria and the implications of different convergence rates, emphasizing the importance of the stopping criterion. The lecture also delves into the Newton method and its relation to fixed point iterations, highlighting the significance of local convergence and the modified Newton method.