Some variants of King's fourth-order family of methods for nonlinear equations

Applied Mathematics and Computation

Volumn 190, Issue 1, 2007, Pages 57-62

  Chun, Changbum ^a  

^a Korea University of Technology and Education   (South Korea)

Author keywords

Iterative methods; King's method; Newton's method; Nonlinear equations; Order of convergence

Indexed keywords

COMPUTATIONAL METHODS; FUNCTION EVALUATION; NONLINEAR EQUATIONS; PROBLEM SOLVING;

ORDER OF CONVERGENCE; TRAUB-OSTROWSKI METHODS;

NUMERICAL METHODS;

EID: 34249774592     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.01.006     Document Type: Article

References (12)

1. Ostrowski A.M. Solution of Equations in Euclidean and Banach Space (1973), Academic Press, New York
2. Chun C. Construction of Newton-like iteration methods for solving nonlinear equations. Numer. Math. 104 3 (2006) 297-315
3. C. Chun, Y. Ham, A one-parameter fourth-order family of iterative methods for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.11.113.
4. C. Chun, Certain improvements of Chebyshev-Halley methods with accelerated fourth-order convergence, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.11.118.
5. W. Gautschi, Numerical Analysis: An introduction, Birkhäuser, 1997.
6. King R. A family of fourth-order methods for nonlinear equations. SIAM J. Numer. Anal. 10 5 (1973) 876-879
7. J. Kou, Y. Li, X. Wang, A variant of super-Halley method with accelerated fourth-order convergence, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.07.118.
8. J. Kou, Y. Li, X. Wang, Fourth-order iterative methods free from second derivative, Appl. Math. Comput. (2006) in press, doi:10.1016/j.amc.2006.05.189.
9. M.A. Noor, F. Ahmad, Fourth-order convergent iterative method for nonlinear equation, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.04.068.
10. Sharma J.R., and Goyal R.K. Fourth-order derivative-free methods for solving non-linear equations. Int. J. Comput. Math. 83 1 (2006) 101-106
11. Argyros I.K., Chen D., and Qian Q. The Jarratt method in Banach space setting. J. Comput. Appl. Math. 51 (1994) 103-106
12. Traub J.F. Iterative Methods for the Solution of Equations (1977), Chelsea publishing company, New York