In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the Hermite inverse interpolation polynomial of degree 2. We study the convergence of the iterative method and we provide new convergence conditions which lead to bilateral approximations for the solution; it is known that the bilateral approximations have the advantage of offering a posteriori bounds of the errors. The numerical examples confirm the advantage of considering these error bounds.
I. Păvăloiu, E. Cătinaş, On a Steffensen-Hermite method of order three, Appl. Math. Comput., 215 (2009) 7, pp. 2663-2672.
PDF-LaTeX version of the paper (soon).
Paper in html form
 S. Amat, J. Blenda, S. Busquier, A Steffensen’s type method with modified functions, Rev. Math. Univ. Parma 7 (2007) 125–133.
 S. Amat, S. Busquier, A two step Steffensen’s method under modified convergence conditions, J. Math. Anal. Appl. 324 (2006) 1084–1092.
 D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variant of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684.
 E. Catinas, The inexact, inexact perturbed and quasi Newton methods are equivalent models, Math. Comput. 74 (2005) 291–301.
 E. Catinas, Methods of Newton and Newton–Krylov type, Ed. Risoprint Cluj-Napoca, Romania, 2007.
 M. Grau, An improvement to the computing of nonlinear equation solution, Numer. Algor. 34 (2003) 1–12.
 Jisheng Kou, Yitian Li, Some variants of Chebyshev–Halley method with fifth-order convergence, Appl. Math. Comput. 189 (2007) 49–54.
 Jisheng Kou, Yitian Li, Modified Chebyshev–Halley methods with sixth-order convergence, Appl. Math. Comput. 188 (2007) 681–685.
 Jisheng Kou, Yitian Li, Xiuhua Wang, Some modifications of Newton’s method with fifth-order convergence, J. Comput. Appl. Math. 209 (2007) 146– 152.
 Nour Mahammand Aslom, Khalida Inayat, Fifth-order iterative method for solving nonlinear equations, Appl. Math. Comput. 188 (2007) 406–410.
 R.J. Sharma, A composite third order Newton–Steffensen method for solving nonlinear equations, Appl. Math. Comput. 169 (2005) 242–246.
 M. Frontini, Hermite interpolation and new iterative method for the computation of the roots of nonlinear equations, Calcolo. 40 (2003) 100–119.
 I. Pavaloiu, On a Steffensen–Hermite type method for approximating the solutions of nonlinear equations, Rev. Anal. Numér. Théor. Approx. 35 (2006) 87–94.
 I. Pavaloiu, Approximation of the root of equations by Aitken–Steffensen-type monotonic sequences, Calcolo. 32 (1995) 69–82.
 I. Pavaloiu, in: Dacia (Ed.), Solution of Equations by Interpolation, Cluj-Napoca, 1981 (in Romanian).
 I. Pavaloiu, E. Catinas, On a Steffensen type method, IEEE Computer Society, Proceedings of SYNASC 2007, 9th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, September 26–29, 2007, pp. 369–375.
 I. Pavaloiu, N. Pop, Interpolation and Applications, Ed. Risoprint Cluj-Napoca, 2005 (in Romanian).
 A. Ostrowski, Solution of Equations in Euclidian and Banach spaces, Academic Press, New York and London, 1973.
 A.B. Turowicz, Sur la dérivée d’ordre superieur d’une fonction inverse, Ann. Polon. Math. 8 (1960) 265–269.