On Broyden-like update via some quadratures for solving nonlinear systems of equations

In this work, we propose a new alternative approximation based on the quasi-Newton approach for solving systems of nonlinear equations using the average of midpoint and Simpson s quadrature. Our goal is to enhance the efficiency of the method (Broyden s method) by reducing the number of iterations it takes to reach a solution. Local convergence analysis and computational results showing the relative efficiency of the proposed method are given.