Modified Chebyshev-Halley methods with sixth-order convergence

Applied Mathematics and Computation

Volumn 188, Issue 1, 2007, Pages 681-685

  Kou, Jisheng ^a   Li, Yitian ^a  

^a WUHAN UNIVERSITY   (China)

Author keywords

Chebyshev Halley methods; Iterative method; Newton's method; Non linear equations; Root finding

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; ROOT LOCI;

CHEBYSHEV HALLEY METHODS; ROOT FINDING; SIXTH ORDER CONVERGENCE;

CHEBYSHEV APPROXIMATION;

EID: 34247646002     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.10.018     Document Type: Article

References (11)

1. Ostrowski A.M. Solution of Equations in Eucilidean and Banach Space. third ed. (1973), Academic Press, New York
2. Gutiérrez J.M., and Hernández M.A. A family of Chebyshev-Halley type methods in Banach spaces. Bull. Austral. Math. Soc. 55 (1997) 113-130
3. Traub J.F. Iterative Methods for Solution of Equations (1964), Prentice-Hall, Englewood CliJs, NJ
4. Argyros I.K. A note on the Halley method in Banach spaces. Appl. Math. Comput. 58 (1993) 215-224
5. Chen D., Argyros I.K., and Qian Q.S. A local convergence theorem for the super-Halley method in a Banach space. Appl. Math. Lett. 7 5 (1994) 49-52
6. Gutiérrez J.M., and Hernández M.A. An acceleration of Newton's method: super-Halley method. Appl. Math. Comput. 117 (2001) 223-239
7. Amat S., Busquier S., and Gutiérrez J.M. Geometric constructions of iterative functions to solve nonlinear equations. J. Comput. Appl. Math. 157 (2003) 197-205
8. Grau M., and Díaz-Barrero J.L. An improvement of the Euler-Chebyshev iterative method. J. Math. Anal. Appl. 315 (2006) 1-7
9. Kou J., Li Y., and Wang X. A family of fifth-order iterations composed of Newton and third-order methods. Appl. Math. Comput. (2006) 10.1016/j.amc.2006.07.150
10. Gautschi W. Numerical Analysis: an Introduction (1997), Birkhäuser, Basel
11. Weerakoon S., and Fernando T.G.I. A variant of Newton's method with accelerated third-order convergence. Appl. Math. Lett. 13 (2000) 87-93