Quasi-Newton methods for nonlinear systems of equations

In this work, we give rise to the motivation of the root-finding problem and the use of Newton’s method within this context. Then, we discuss why one might go beyond those methods to introduce Quisi-Newton methods to which we rigorously derive both types of Broyden Updates along with an efficient implementation of the algorithm. We run my implementation of both types of Broyden Updates along with Newton’s method and an implementation of Broyden Updates provided by the Scipy library on two realistic real-world problems. We finally discuss the application of Broyden Updates in many different areas of science and the different variants of the algorithm that were later proposed.