On the efficiency of the computations for approximating the solutions of equations

We consider the iterative methods for solving nonlinear equations in \(\mathbb{R}\) and the class of iterative methods obtained by inverse interpolation of Taylor type; we determine the iterative method having the greatest efficiency index. We show that this method is the Chebyshev method given by the second degree interpolatory polynomial for the inverse function.

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

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I. Păvăloiu, On the efficiency of the computations for approximating the solutions of equations, Bul. Ştiinţ. Univ. Baia Mare, Ser. B Mat.-Inf., 14 (1998) no. 1, pp. 59-64.