Quadrature based Broyden-like method for systems of nonlinear equations

A new iterative method based on the quasi-Newton approach for solving systems of nonlinear equations, especially large scale is proposed. We used the weighted combination of the Trapezoidal and Simpson quadrature rules. Our goal is to enhance the efficiency of the well known Broyden method by reducing the number of iterations it takes to reach a solution. Local convergence analysis and computational results are given