Modified Ostrowski's method with eighth-order convergence and high efficiency index

Applied Mathematics Letters

Volumn 23, Issue 5, 2010, Pages 549-554

  Wang, Xia ^a   Liu, Liping ^b  

^a ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY   (China)

^b NORTH CAROLINA A AND T STATE UNIVERSITY   (United States)

Author keywords

Convergence order; Efficiency index; Hermite interpolation; Nonlinear equations; Ostrowski's method

Indexed keywords

CONVERGENCE ORDER; EFFICIENCY INDEX; FIRST DERIVATIVE; HERMITE INTERPOLATION; HERMITE INTERPOLATION METHOD; HIGH EFFICIENCY; ILLUSTRATIVE EXAMPLES; NEWTON'S METHODS; NUMERICAL COMPARISON; SIMPLE ROOT;

INTERPOLATION; NEWTON-RAPHSON METHOD;

NONLINEAR EQUATIONS;

EID: 77949484764     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.01.009     Document Type: Article

References (26)

1. Ostrowski A.M. Solution of Equations in Euclidean and Banach Space. third ed. (1973), Academic Press, New York
2. Kung, and Traub. Optimal order of one-point and multipoint iterations. J. Appl. Comput. Math. 21 (1974) 643-651
3. Chun C., and Ham Y. Some sixth-order variants of Ostrowski root-finding methods. Appl. Math. Comput. 193 (2007) 389-394
4. Kou J., Li Y., and Wang X. Some variants of Ostrowskis method with seventh-order convergence. J. Comput. Appl. Math. 209 (2007) 153-159
5. Bi W., Ren H., and Wu Q. Three-step iterative methods with eighth-order convergence for solving nonlinear equations. J. Comput. Appl. Math. 225 (2009) 105-112
6. Bi W., Wu Q., and Ren H. A new family of eighth-order iterative methods for solving nonlinear equations. Appl. Math. Comput. 214 (2009) 236-245
7. R. Thukral, M.S. Petković, A family of three-point methods of optimal order for solving nonlinear equations, J. Comput. Appl. Math. (in press) Corrected Proof, Available online 12 October 2009.
8. Liping Liu, Xia Wang, Eighth-order methods with high efficiency index for solving nonlinear equations, Appl. Math. Comput. (in press) Corrected Proof, Available online 6 November 2009.
9. Kou J., Wang X., and Li Y. Some eighth-order root finding three-step methods. Commun. Nonlinear Sci. Numer. Simul. 15 3 (2010) 536-544
10. Özban A.Y. Some new variants of Newton's method. Appl. Math. Lett. 17 (2004) 677-682
11. Thukral R. Introduction to a Newton-type method for solving nonlinear equations. Appl. Math. Comput. 195 (2008) 663-668
12. 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
13. Chun C. Construction of third-order modifications of Newton's method. Appl. Math. Comput. 189 (2007) 662-668
14. Chun C. Some fourth-order iterative methods for solving nonlinear equations. Appl. Math. Comput. 195 (2008) 454-459
15. Chun C., and Ham Y. Some second-derivative-free variants of super-Halley method with fourth-order convergence. Appl. Math. Comput. 195 (2008) 537-541
16. Kou J., and Li Y. The improvements of Chebyshev-Halley methods with fifth-order convergence. Appl. Math. Comput. 188 (2007) 143-147
17. Ham Y., and Chun C. A fifth-order iterative method for solving nonlinear equations. Appl. Math. Comput. 194 (2007) 287-290
18. Kou J., and Li Y. Modified Chebyshev-Halley methods with sixth-order convergence. Appl. Math. Comput. 188 (2007) 681-685
19. Kou J., and Li Y. An improvement of the Jarratt method. Appl. Math. Comput. 189 (2007) 1816-1821
20. Wang X., Kou J., and Li Y. A variant of Jarratt method with sixth-order convergence. Appl. Math. Comput. 204 (2008) 14-19
21. Chun C. Some improvements of Jarratt's method with sixth-order convergence. Appl. Math. Comput. 190 (2007) 1432-1437
22. Kou J. Some new sixth-order methods for solving non-linear equations. Appl. Math. Comput. 189 (2007) 647-651
23. Chun C., and Neta B. Some modifications of Newton's method by the method of undetermined coefficients. Comput. Math. Appl. 56 (2008) 2528-2538
24. Wang X., and Liu L. Two new families of sixth-order methods for solving non-linear equations. Comput. Math. Appl. 213 1 (2009) 73-78
25. Ham Y., Chun C., and Lee S.-G. Some higher-order modifications of Newton's method for solving nonlinear equations. J. Comput. Appl. Math. 222 (2008) 477-486
26. Gautschi W. Numerical Analysis: An Introduction (1997), Birkhauser