A class of Steffensen type methods with optimal order of convergence

Applied Mathematics and Computation

Volumn 217, Issue 19, 2011, Pages 7653-7659

  Cordero, Alicia ^a   Torregrosa, Juan R ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

Convergence order; Derivative free method; Efficiency index; Iterative methods; Nonlinear equations; Steffensen's method

Indexed keywords

CLASS OF METHODS; CONVERGENCE ORDER; DERIVATIVE FREE METHOD; DERIVATIVE-FREE; DIVIDED DIFFERENCE; EFFICIENCY INDEX; FOURTH-ORDER; FUNCTIONAL EVALUATION; LINEAR COMBINATIONS; MULTI-POINT METHODS; NONSMOOTH EQUATION; NUMERICAL EXAMPLE; OPTIMAL ORDER OF CONVERGENCE; ORDER OF CONVERGENCE; STEFFENSEN'S METHOD; TYPE METHODS;

FUNCTION EVALUATION; NONLINEAR EQUATIONS;

NUMERICAL METHODS;

EID: 79955824744     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.02.067     Document Type: Article

References (12)

1. J.M. Ortega, and W.G. Rheinboldt Iterative Solutions of Nonlinear Equations in Several Variables 1970 Academic Press New York
2. P. Jain Steffensen type methods for solving nonlinear equations Applied Mathematics and Computation 194 2007 527 533 (Pubitemid 350088994)
3. M. Dehghan, and M. Hajarian An Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations Journal of Computational and Applied Mathematics 29 2010 19 30
4. H. Ren, Q. Wu, and W. Bi A class of two-step Steffensen type methods with fourth-order convergence Applied Mathematics and Computation 209 2009 206 210
5. Q. Zheng, J. Wang, P. Zhao, and L. Zhang A Steffensen-like method and its higher-order variants Applied Mathematics and Computation 214 2009 10 16
6. X. Feng, and Y. He High order oterative methods without derivatives for solving nonlinear equations Applied Mathematics and Computation 186 2007 1617 1623 (Pubitemid 46497369)
7. A.M. Ostrowski Solutions of Equations and Systems of Equations 1966 Academic Press New York-London
8. H.T. Kung, and J.F. Traub Optimal order of one-point and multi-point iteration Applied Mathematics and Computation 21 1974 643 651
9. S. Amat, and S. Busquier On a Steffensen's type method and its behavior for semismooth equations Applied Mathematics and Computation 177 2006 819 823 (Pubitemid 44172899)
10. F.A. Potra, L. Qi, and D. Sun Secant methods for semismooth equations Numerical Mathematics 80 1998 305 324
11. A. Cordero, and J.R. Torregrosa Variants of Newton's method using fifth-order quadrature formulas Applied Mathematics and Computation 190 2007 686 698 (Pubitemid 46856698)
12. S. Amat, and S. Busquier On a higher order secant methods Applied Mathematics and Computation 141 2003 321 329