Some higher-order modifications of Newton's method for solving nonlinear equations

Journal of Computational and Applied Mathematics

Volumn 222, Issue 2, 2008, Pages 477-486

  Ham, YoonMee ^a   Chun, Changbum ^b   Lee, Sang Gu ^b  

^a Kyonggi University   (South Korea)

^b Sungkyunkwan University   (South Korea)

Author keywords

Iterative methods; Modified Newton's method; Newton's method; Nonlinear equations; Order of convergence; Root finding

Indexed keywords

BOOLEAN FUNCTIONS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; FUNCTIONS; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS;

MODIFIED NEWTON'S METHOD; NEWTON'S METHOD; ORDER OF CONVERGENCE; ROOT-FINDING;

ITERATIVE METHODS;

EID: 53449084497     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.11.018     Document Type: Article

References (19)

1. Chun C. Construction of Newton-like iteration metods for solving nonlinear equations. Numer. Math. 104 2 (2006) 297-315
2. Chun C., and Ham Y. Some sixth-order variants of Ostrowski root-finding methods. Appl. Math. Comput. 193 2 (2007) 389-394
3. Gautschi W. Numerical Analysis: An Introduction (1997), Birkhäuser
4. Grau M., and Díaz-Barrero J.L. An improvement to Ostrowski root-finding method. Appl. Math. Comput. 173 1 (2006) 450-456
5. Grau M., and Díaz-Barrero J.L. An improvement of the Euler-Chebyshev iterative method. J. Math. Anal. Appl. 315 1 (2006) 1-7
6. Grau-Sánchez M. Improvements of the efficiency of some three-step iterative like-Newton methods. Numer. Math. 107 1 (2007) 131-146
7. Homeier H.H.H. On newton-type methods with cubic convergence. J. Comput. Appl. Math. 176 2 (2005) 425-432
8. Kanwar M.V., Kukreja V.K., and Singh S. On a class of quadratically convergent iteration formulae. Appl. Math. Comput. 66 3 (2006) 633-637
9. Kou J., Li Y., and Wang X. A family of fifth-order iterations composed of Newton and third-order methods. Appl. Math. Comput. 186 2 (2007) 1258-1262
10. Kou J., and Li Y. The improvements of Chebyshev-Halley methods with fifth-order convergence. Appl. Math. Comput. 188 1 (2007) 143-147
11. Kou J., and Li Y. Modified Chebyshev-Halley methods with sixth-order convergence. Appl. Math. Comput. 188 1 (2007) 681-685
12. Kou J. The improvements of modified Newton's method. Appl. Math. Comput. 189 1 (2007) 602-609
13. Kou J., Li Y., and Wang X. Some new sixth-order methods for solving non-linear equations. Appl. Math. Comput. 189 1 (2007) 647-651
14. Noor M.A., and Noor K.I. Fifth-order iterative methods for solving nonlinear equations. Appl. Math. Comput. 188 1 (2007) 406-410
15. Noor K.I., and Noor M.A. Predictor-corrector Halley method for nonlinear equation. Appl. Math. Comput. 188 2 (2007) 1587-1591
16. Noor M.A., Khan W.A., and Hussain A. A new modified Halley method without second derivatives for nonlinear equation. Appl. Math. Comput. 189 2 (2007) 1268-1273
17. Traub J.F. Iterative Methods for the Solution of Equations (1977), Chelsea Publishing Company, New York
18. Vy D.T. A fifth-order iterative method for solving equations. Acta Math. Hungar. 49 1-2 (1987) 129-137
19. Weerakoon S., and Fernando T.G.I. A variant of Newton's method with accelerated third-order convergence. Appl. Math. Lett. 13 8 (2000) 87-93