References
- Amat , S. , Busquier , S. and Hernández , M. A. 2003 . Geometric constructions of iterative functions to solve nonlinear equations . J. Comput. Appl. Math. , 157 : 197 – 205 .
- Argyros , I. K. 1993 . A note on the Halley method in Banach spaces . Appl. Math. Comput. , 58 : 215 – 224 .
- Chen , D. , Argyros , I. K. and Qian , Q. S. 1994 . A local convergence theorem for the super-Halley method in a Banach space . Appl. Math. Lett. , 7 : 49 – 52 .
- Chun , C. 2007 . A method for obtaining iterative formulas of order three . Appl. Math. Lett. , 20 : 1103 – 1109 .
- Gautschi , W. 1997 . Numerical Analysis: An Introduction , Boston, MA : Birkhäuser .
- Gutiérrez , J. M. and Hernández , M. A. 2001 . An acceleration of Newton's method: super-Halley method . Appl. Math. Comput. , 117 : 223 – 239 .
- Hansen , E. and Patrick , M. 1977 . A family of root finding methods . Numer. Math. , 27 : 257 – 269 .
- Jarratt , P. 1966 . Some fourth order multipoint iterative methods for solving equations . Math. Comput. , 20 : 434 – 437 .
- Lukić , T. and Ralević , N. M. 2008 . Geometric mean Newton's method for simple and multiple roots . Appl. Math. Lett. , 21 : 30 – 36 .
- Ostrowski , A. M. 1973 . Solutions of Equations and System of Equations , 3 , New York : Academic Press .
- Potra , F. A. and Pták , V. 1984 . Nondiscrete Induction and Iterative Processes , Boston : Pitman . Research Notes in Mathematics Vol. 103
- Traub , J. F. 1964 . “ Iterative Methods for the Solution of Equations ” . Englewood Cliffs, NJ : Prentice Hall .
- Traub , J. F. 1972 . Computational complexity of iterative processes . SIAM J. Comput. , 1 : 167 – 179 .
- Weerakoon , S. and Fernando , T. G.I. 2000 . A variant of Newton's method with accelerated third-order convergence . Appl. Math. Lett. , 13 : 87 – 93 .