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