A family of fifth-order iterations composed of Newton and third-order methods

Applied Mathematics and Computation

Volumn 186, Issue 2, 2007, Pages 1258-1262

  Kou, Jisheng ^a   Li, Yitian ^a   Wang, Xiuhua ^a  

^a WUHAN UNIVERSITY   (China)

Author keywords

Chebyshev's method; Halley's method; Iterative method; Newton's method; Non linear equations; Super Halley method

Indexed keywords

CHEBYSHEV APPROXIMATION; DIFFERENTIATION (CALCULUS); NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

HALLEY'S METHOD; SECOND DERIVATIVE; SUPER-HALLEY METHOD; THIRD-ORDER METHODS;

ITERATIVE METHODS;

EID: 33947709556     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.07.150     Document Type: Article

References (10)

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. Gutiérrez J.M., and Hernández M.A. An acceleration of Newton's method: Super-Halley method. Appl. Math. Comput. 117 (2001) 223-239
6. 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
7. Ezquerro J.A., Gutiérrez J.M., Hernández M., and Salanova M.A. Chebyshev-like methods and quadratic equations. Rev. Anal. Numér. Théor. Approx. 28 1 (1999) 23-35
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. Gautschi W. Numerical Analysis: an Introduction (1997), Birkhäuser
10. 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