Newton method for systems: Fixed point iterations

This lecture covers the Newton method for systems and fixed point iterations, discussing the convergence of fixed point methods and the global convergence of the Newton method. It explains the algorithm, stopping criteria, and the properties of the Newton method for systems. The lecture also explores the convergence of the method, the role of the Jacobian matrix, and the conditions for the existence of fixed points. Additionally, it delves into the concept of neighborhood convergence and the estimation of errors in the method.