참고문헌
- S. Amat, A. A. Magrenan, and N. Romero, On a two-step relaxed Newton-type method, App. Math. Comput. 219 (2013), no. 24, 11341-11347. https://doi.org/10.1016/j.amc.2013.04.061
- I. K. Argyros, Computational theory of iterative methods, Series: Studies in Computational Mathematics, 15, Editors: C. K. Chui and L. Wuytack, Elsevier Publ. Co. New York, U.S.A, 2007.
- I. K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton's method, J. Complexity 28 (2012), no. 3, 364-387. https://doi.org/10.1016/j.jco.2011.12.003
- I. K. Argyros and S. Hilout, Computational Methods in Nonlinear Analysis, World Scientific Publ. Comp., New Jersey, 2013.
- V. Candela and A. Marquina, Recurrence relations for rational cubic methods I: The Halley method, Computing 44 (1990), no. 2, 169-184. https://doi.org/10.1007/BF02241866
- V. Candela and A. Marquina, Recurrence relations for rational cubic methods II: The Chebyshev method, Computing 45 (1990), no. 4, 355-367. https://doi.org/10.1007/BF02238803
- C. Chun, P. Stanica, and B. Neta, Third order family of methods in Banach spaces, Comput. Math. Appl. 61 (2011), no. 6, 1665-1675. https://doi.org/10.1016/j.camwa.2011.01.034
- J. A. Ezquerro and M. A. Hernandez, Recurrence relations for Chebyshev-type methods, Appl. Math. Optim. 41 (2000), no. 2, 227-236. https://doi.org/10.1007/s002459911012
- J. M. Gutierrez and M. A. Hernandez, Recurrence relations for the super-Halley method, Computers Math. Appl. 36 (1998), no. 7, 1-8.
- J. M. Gutierrez and M. A. Hernandez, Third-order iterative methods for operators with bounded second derivative, J. Comput. Appl. Math. 82 (1997), no. 1-2, 171-183. https://doi.org/10.1016/S0377-0427(97)00076-9
- J. M. Gutierrez, A. A. Magrenan, and N. Romero, On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions, Appl. Math. Comput. 221 (2013), 79-88. https://doi.org/10.1016/j.amc.2013.05.078
- L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
- J. S. Kou and T. Li, Modified Chebyshev's method free from second derivative for non-linear equations, Appl. Math. Comput. 187 (2007), no. 2, 1027-1032. https://doi.org/10.1016/j.amc.2006.09.021
- J. S. Kou, T. Li, and X. H. Wang, A modification of Newton method with third-order convergence, Appl. Math. comput. 181 (2006), no. 2, 1106-1111. https://doi.org/10.1016/j.amc.2006.01.076
- A. A. Magrenan, Estudio de la dinamica del metodo de Newton amortiguado, PhD Thesis, Servicio de Publicaciones, Universidad de La Rioja, 2013.
- A. A. Magrenan and I. K. Argyros, Two-step Newton methods, J. Complexity 30 (2014), no. 4, 533-553. https://doi.org/10.1016/j.jco.2013.10.002
- J. M. Ortega andW. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic press, New York, 1970.
- P. K. Parida, Study of some third order methods for nonlinear equations in Banach spaces, Ph.D. Dessertation, Indian Institute of Technology, Department of Mathematics, Kharagpur, India, 2007.
- P. K. Parida and D. K. Gupta, Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces, J. Math. Anal. Appl. 345 (2008), 350-361. https://doi.org/10.1016/j.jmaa.2008.03.064
- F. A. Potra and V. Ptra, Nondiscrete induction and iterative processes, in Research Notes in Mathematics, Vol. 103, Pitman, Boston, 1984.
- L. B. Rall, Computational solution of nonlinear operator equations, Robert E. Krieger, New York, 1979.
- Q. Wu and Y. Zhao, Third order convergence theorem by using majorizing function for a modified Newton method in Banach space, Appl. Math. Comput. 175 (2006), no. 2, 1515-1524. https://doi.org/10.1016/j.amc.2005.08.043