On the convergence of Broyden’s method for nonlinear systems of equations

Abstract

This paper uses majorant techniques to study the convergence of Broyden’s single-rank update method for nonlinear systems of equations. It also contains a very elementary proof of the local convergence of the method. The heart of the method is a procedure for generating an approximation to the Jacobian of the system using only information on hand and not requiring partial derivatives.