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Sixth-order variants of Chebyshev-Halley methods for solving non-linear equations. (English) Zbl 1122.65339
Summary: We present a family of new variants of Chebyshev-Halley methods with sixth-order convergence. Compared with Chebyshev-Halley methods, the new methods require one additional evaluation of the function. The numerical results presented show that the new methods compete with Chebyshev-Halley methods.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Ostrowski, A. M.: Solutions of equations and system of equations. (1960) · Zbl 0115.11201
[2] Gutiérrez, J. M.; Hernández, M. A.: A family of Chebyshev -- halley type methods in Banach spaces. Bull. aust. Math. soc. 55, 113-130 (1997) · Zbl 0893.47043
[3] Traub, J. F.: Iterative methods for solution of equations. (1964) · Zbl 0121.11204
[4] Argyros, I. K.: A note on the halley method in Banach spaces. Appl. math. Comput. 58, 215-224 (1993) · Zbl 0787.65034
[5] Chen, D.; Argyros, I. K.; Qian, Q. S.: A local convergence theorem for the super -- halley method in a Banach space. App. math. Lett. 7, No. 5, 49-52 (1994) · Zbl 0811.65043
[6] Gutiérrez, J. M.; Hernández, M. A.: An acceleration of Newton’s method: super -- halley method. Appl. math. Comput. 117, 223-239 (2001) · Zbl 1023.65051
[7] Amat, S.; Busquier, S.; Gutiérrez, J. M.: Geometric constructions of iterative functions to solve nonlinear equations. J. comput. Appl. math. 157, 197-205 (2003) · Zbl 1024.65040
[8] Grau, M.; Dı&acute, J. L.; Az-Barrero: An improvement of the Euler -- Chebyshev iterative method. J. math. Anal. appl. 315, 1-7 (2006)
[9] Kou, Jisheng; Li, Yitian; Wang, Xiuhua: A family of fifth-order iterations composed of Newton and third-order methods. Appl. math. Comput. (2006) · Zbl 1119.65037
[10] Kou, Jisheng; Li, Yitian: The improvements of Chebyshev -- halley methods with fifth-order convergence. Appl. math. Comput. (2006) · Zbl 1118.65036
[11] Kou, Jisheng; Li, Yitian: Some variants of Chebyshev -- halley methods with fifth-order convergence. Appl. math. Comput. (2006) · Zbl 1122.65336
[12] Kou, Jisheng; Li, Yitian: Modified Chebyshev -- halley methods with sixth-order convergence. Appl. math. Comput. (2006) · Zbl 1118.65037
[13] Kou, Jisheng: Some new sixth-order methods for solving non-linear equations. Appl. math. Comput. (2006) · Zbl 1122.65333
[14] Kou, Jisheng: On Chebyshev -- halley methods with sixth-order convergence for solving nonlinear equations. Appl. math. Comput. (2007) · Zbl 1122.65334
[15] Chun, C.: Certain improvements of Chebyshev -- halley methods with accelerated fourth-order convergence. Appl. math. Comput. (2007) · Zbl 1122.65324
[16] Gautschi, W.: Numerical analysis: an introduction. (1997) · Zbl 0877.65001
[17] Weerakoon, S.; Fernando, T. G. I.: A variant of Newton’s method with accelerated third-order convergence. Appl. math. Lett. 13, 87-93 (2000) · Zbl 0973.65037