Efficient Steffensen-type algorithms for solving nonlinear equations

We introduce a Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting. Then, we present a local convergence analysis for (STTM) using recurrence relations. Numerical examples validating our theoretical results are also provided in this study to show that (STTM) is faster than other methods [I.K. Argyros, J. Ezquerro, J.M. Gutiérrez, M. Hernández, and S. Hilout, On the semilocal convergence of efficient Chebyshev-Secant-type methods, J. Comput. Appl. Math. 235 (2011), pp. 3195–3206; J.A. Ezquerro and M.A. Hernández, An optimization of Chebyshev's method, J. Complexity 25 (2009), pp. 343–361] using similar convergence conditions.

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