Construction of third-order modifications of Newton's method

Applied Mathematics and Computation

Volumn 189, Issue 1, 2007, Pages 662-668

  Chun, Changbum ^a  

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

Author keywords

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

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NONLINEAR EQUATIONS; THEOREM PROVING;

ITERATION FORMULAS; NEWTON'S METHOD; THIRD ORDER METHODS;

ITERATIVE METHODS;

EID: 34248403767     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.11.127     Document Type: Article

References (11)

1. Potra F.A., and Pták V. Nondiscrete induction and iterative processes. Research Notes in Mathematics vol. 103 (1984), Pitman, Boston
2. Weerakoon S., and Fernando G.I. A variant of Newton's method with accelerated third-order convergence. Appl. Math. Lett. 17 (2000) 87-93
3. Frontini M., and Sormani E. Some variants of Newton's method with third-order convergence. J. Comput. Appl. Math. 140 (2003) 419-426
4. Homeier H.H.H. On Newton-type methods with cubic convergence. J. Comput. Appl. Math. 176 (2005) 425-432
5. Özban A.Y. Some new variants of Newton's method. Appl. Math. Lett. 17 (2004) 677-682
6. J. Kou, Y. Li, X. Wang, A modification of Newton method with third-order convergence, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.01.076.
7. Traub J.F. Iterative Methods for the Solution of Equations (1977), Chelsea Publishing Company, New York
8. Householder A.S. The Numerical Treatment of a Single Nonlinear Equation (1970), McGraw-Hill, New York
9. Mamta, Kanwar V., Kukreja V.K., and Singh S. On a class of quadratically convergent iteration formulae. Appl. Math. Comput. 166 3 (2006) 633-637
10. Chen J., and Li W. On new exponential quadratically convergent iteration formulae. Appl. Math. Comput. 180 1 (2006) 242-246
11. Wu X.-Y. A new continuation Newton-like method and its deformation. Appl. Math. Comput. 112 (2000) 75-78