Abstract
In this paper, a one-step Steffensen-type method of order 3.383 is designed and proved for solving nonlinear equations. This super-cubic convergence is obtained by self-accelerating second-order Steffensen's method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Numerical examples confirm the theoretical results and high computational efficiency.
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