It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled nodes. The chord method is an interpolatory method, with two distinct nodes. Using this remark, the Steffensen and Aitken-Steffensen methods have been generalized using interpolatory methods obtained from the inverse interpolation polynomial of Lagrange or Hermite type. In this paper we study the convergence and efficiency of some Steffensen type methods which are obtained from the inverse interpolatory polynomial of Hermite type with two controlled nodes.
nonlinear equations in R; Steffensen and Aitken-Steffensen methods; inverse interpolatory polynomial of Hermite type
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I. Păvăloiu, On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations, Rev. Anal. Numér. Théor. Approx. 35 (2006) no. 1, pp. 87-94.