Two derivative-free algorithms for nonlinear equations

In this paper, we propose two new derivative-free algorithms for nonlinear equations. The first is based on quasi-Newton method and is globally and superlinearly convergent under some mild assumptions. The second combines the ideas of the first with the filter strategy, which helps to reduce the backtracking steps in calculating the stepsizes, for evaluating candidate points. We show its convergence under the same assumptions. The resulting algorithms show some attractive features. Some encouraging preliminary computational results for both algorithms are reported.