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Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains


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[1] Argyros I.K., On the Newton–Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 169 (2004), 315–332.10.1016/j.cam.2004.01.029Search in Google Scholar

[2] Argyros I.K., Ezquerro J.A., Gutiérrez J.M., Hernández M.A., Hilout S., On the semilocal convergence of efficient Chebyshev-Secant-type methods, J. Comput. Appl. Math. 235 (2011), 3195–3206.10.1016/j.cam.2011.01.005Search in Google Scholar

[3] Argyros I.K., Ren H., Efficient Steffensen-type algorithms for solving nonlinear equations, Int. J. Comput. Math. 90 (2013), 691–704.10.1080/00207160.2012.737461Open DOISearch in Google Scholar

[4] Argyros I.K., Computational Theory of Iterative Methods, Studies in Computational Mathematics, 15, Elsevier B.V., New York, 2007.Search in Google Scholar

[5] Ezquerro J.A., Hernández M.A., An optimization of Chebyshev’s method, J. Complexity 25 (2009), 343–361.10.1016/j.jco.2009.04.001Open DOISearch in Google Scholar

[6] Ezquerro J.A., Grau A., Grau-Sánchez M., Hernández M.A., Construction of derivative-free iterative methods from Chebyshev’s method, Anal. Appl. (Singap.) 11 (2013), 1350009, 16 pp.10.1142/S0219530513500097Search in Google Scholar

[7] Ezquerro J.A., Gutiérrez J.M., Hernández M.A., Salanova M.A., Chebyshev-like methods and quadratic equations, Rev. Anal. Numér. Théor. Approx. 28 (1999), 23–35.Search in Google Scholar

[8] Grau M., Díaz-Barrero J.L., An improvement of the Euler–Chebyshev iterative method, J. Math. Anal. Appl. 315 (2006), 1–7.10.1016/j.jmaa.2005.09.086Search in Google Scholar

[9] Grau-Sánchez M., Gutiérrez J.M., Some variants of the Chebyshev–Halley family of methods with fifth order of convergence, Int. J. Comput. Math. 87 (2010), 818–833.10.1080/00207160802208358Search in Google Scholar

[10] Hueso J.L., Martinez E., Teruel C., Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems, J. Comput. Appl. Math. 275 (2015), 412–420.10.1016/j.cam.2014.06.010Search in Google Scholar

[11] Magreñán Á.A., Estudio de la dinámica del método de Newton amortiguado, PhD Thesis, Universidad de La Rioja, Servicio de Publicaciones, Logroño, 2013. Available at http://dialnet.unirioja.es/servlet/tesis?codigo=38821Search in Google Scholar

[12] Magreñán Á.A., Different anomalies in a Jarratt family of iterative root-finding methods, Appl. Math. Comput. 233 (2014), 29–38.Search in Google Scholar

[13] Magreñán Á.A., A new tool to study real dynamics: the convergence plane, Appl. Math. Comput. 248 (2014), 215–224.Search in Google Scholar

[14] Prashanth M., Mosta S.S., Gupta D.K., Semi-local convergence of the Supper-Halley’s method under w-continuous second derivative in Banach space. Submitted.Search in Google Scholar

[15] Rheinboldt W.C., An adaptive continuation process for solving systems of nonlinear equations, in: Tikhonov A.N., et al. (eds.), Mathematical Models and Numerical Methods, Banach Center Publ., 3, PWN, Warsaw, 1978, pp. 129–142.10.4064/-3-1-129-142Search in Google Scholar

[16] Traub J.F., Iterative Methods for the Solution of Equations, Prentice-Hall Series in Automatic Computation, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1964.Search in Google Scholar

eISSN:
2391-4238
ISSN:
0860-2107
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Mathematics, General Mathematics