Quasi-Newton method for solving nonlinear systems of equations.

What is it about?

We present an alternative Broyden quasi-Newton update for addressing nonlinear systems of equations.

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Why is it important?

We have shown that one can use the approach of approximating Jacobian matrices with Broyden's matrices via a quadrature formula and we obtained an ecient update maintaining the local order of convergence of Broyden's method. Numerical experiments show a strong indication that the newly proposed Broyden-like method exhibits enhanced performance (with respect to the number of iterations) in most of the tested problems by comparison with the other variants. Finally, we can conclude that the use of numerical quadratures to approximate the Newton step is capable of improving the efficiency of the quasi-Newton (Broyden) method to an acceptable level.

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