Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three

[1] S. Amat, S. Busquier, On a Steffensen’s type method and its behavior for semismooth equations, Appl. Math. Comput. 177 (2006) 819–823.

[2] S. Amat, S. Busquier, A two-step Steffensen’s method under modified convergence conditions, J. Math. Anal. Appl. 324 (2006) 1084–1092.

[3] S. Amat, S. Busquier, V. Candela, A class of quasi-Newton generalized Steffensen methods on Banach spaces, J. Comput. Appl. Math. 149 (2002) 397– 406.

[4] I.K. Argyros, A new convergence theorem for the Steffensen method in Banach space and applications, Rev. Anal. Numér. Théor. Approx. 29 (2) (2000) 119–128.

[5] E. Catinas, On some Steffensen-type iterative methods for a class of nonlinear equations, Rev. Anal. Numér. Théor. Approx. 24 (1–2) (1995) 37–43.

[6] E. Catinas, Methods of Newton and Newton-Krylov Type, Risoprint, Cluj-Napoca, 2007.

[7] M. Frontini, Hermite interpolation and a new iterative method for the computation of the roots of non-linear equations, Calcolo 40 (2003) 109–119.

[8] M. Grau, An improvement to the computing of nonlinear equation solution, Numer. Algorithms 34 (2003) 1–12.

[9] P. Jain, Steffensen type methods for solving non-linear equations, Appl. Math. Comput. 194 (2007) 527–533.

[10] M.A. Ostrovski, Solution of Equations and Systems of Equations, Academic Press, New York, 1982.

[11] I. Pavaloiu, Approximation of the root of equations by Aitken–Steffensen-type monotonic sequences, Calcolo 32 (1–2) (1995) 69–82.

[12] I. Pavaloiu, N. Pop, Interpolation and Applications, Risoprint, Cluj-Napoca, Romania, 2005 (in Romanian).

[13] I. Pavaloiu, Bilateral approximations of solutions of equations by order three Steffensen-type methods, Studia Univ. Babes-Bolyai, Mathematica LI (3) (2006) 87–94.

[14] I. Pavaloiu, Optimal efficiency index of a class of Hermite iterative methods with two steps, Rev. Anal. Numér. Théor. Approx. 29 (1) (2009) 83–89.

[15] I. Pavaloiu, E. Catinas, On a Steffensen type method, in: SYNASC 2007, Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE Computer Society, Timisoara, Romania 26–29 September 2007.

[16] I. Pavaloiu, E. Catinas, On a Steffensen–Hermite method of order three, Appl. Math. Comput. 215 (2009) 2663–2672.

[17] J.R. Sharma, A composite third order Newton–Steffensen method for solving nonlinear equations, Appl. Math. Comput. 169 (2005) 342–346.

[18] B.A. Turowicz, Sur le derivées d’ordre superieur d’une fonction inverse, Ann. Polon. Math. 8 (1960) 265–269.