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Local convergence comparison between two novel sixth order methods for solving equations


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[1] Argyros, Ioannis K., Santhosh George and Alberto Á. Magre?án. “Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order.” J. Comput. Appl. Math. 282 (2015): 215-224. Cited on 6 and 16.10.1016/j.cam.2014.12.023Search in Google Scholar

[2] Argyros, Ioannis K., Santhosh George and Narayan Thapa. Mathematical modeling for the solution of equations and systems of equations with applications. Vol. 1. New York: Nova Publishes, 2018. Cited on 6, 9, 12 and 16.Search in Google Scholar

[3] Argyros, Ioannis K., Santhosh George and Narayan Thapa. Mathematical modeling for the solution of equations and systems of equations with applications. Vol. 2. New York: Nova Publishes, 2018. Cited on 6, 9 and 12.Search in Google Scholar

[4] Argyros, Ioannis K., Munish Kansal and V. Kanwar, V. “Local convergence for multipoint methods using only the first derivative.” SeMA J. 73, no. 4 (2016): 369-378. Cited on 6, 8 and 12.10.1007/s40324-016-0075-zSearch in Google Scholar

[5] Candela, V. and A. Marquina. “Recurrence relations for rational cubic methods. I. The Halley method.” Computing 44, no. 2 (1990): 169-184. Cited on 6, 8 and 12.10.1007/BF02241866Search in Google Scholar

[6] Candela, V. and A. Marquina. “Recurrence relations for rational cubic methods. II. The Chebyshev method.” Computing 45, no. 4 (1990): 355-367. Cited on 6 and 12.10.1007/BF02238803Search in Google Scholar

[7] Chen, Jinhai, Ioannis Argyros and Ravi P. Agarwal. “Majorizing functions and two-point Newton-type methods.” J. Comput. Appl. Math. 234, no. 5 (2010): 1473-1484. Cited on 6, 8 and 16.10.1016/j.cam.2010.02.024Search in Google Scholar

[8] Ezquerro, J.A., D. González and M.A. Hernández. “On the local convergence of Newton’s method under generalized conditions of Kantorovich.” Appl. Math. Lett. 26, no. 5 (2013): 566-570. Cited on 6 and 8.10.1016/j.aml.2012.12.012Search in Google Scholar

[9] Gutiérrez, J.M. and M.A. Hernández. “An acceleration of Newton’s method: super-Halley method.” Appl. Math. Comput. 117, no. 2-3, (2001): 223-239. Cited on 6 and 16.10.1016/S0096-3003(99)00175-7Search in Google Scholar

[10] Hernández, M.A. and N. Romero. “On a characterization of some Newton-like methods of R-order at least three.” J. Comput. Appl. Math. 183, no. 1 (2005): 53-66. Cited on 6 and 16.10.1016/j.cam.2005.01.001Search in Google Scholar

[11] Hernández-Verón, M.A. and Eulalia Martínez. “On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions.” Numer. Algorithms 70, no. 2 (2015): 377-392. Cited on 6.10.1007/s11075-014-9952-7Search in Google Scholar

[12] Jarratt, P. “Some fourth order multipoint iterative methods for solving equations.” Math. Comput. 20, no.95 (1966): 434-437. Cited on 6, 12, 13 and 16.10.1090/S0025-5718-66-99924-8Search in Google Scholar

[13] Kantorovich, L.V. and G.P. Akilov. Functional analysis. Oxford-Elmsford, N.Y.: Pergamon Press, 1982. Cited on 6 and 9.Search in Google Scholar

[14] Kumar, Abhimanyu and D.K. Gupta. “Local convergence of Super Halley’s method under weaker conditions on Fréchet derivative in Banach spaces.” J. Anal. (2017) DOI:10.1007/s41478-017-0034-9. Cited on 6 and 8.10.1007/s41478-017-0034-9.Cited68Open DOISearch in Google Scholar

[15] Madhu, Kalyanasundaram. “Sixth order Newton-type method for solving system of nonlinear equations and its applications.” Appl. Math. E-Notes 17 (2017): 221-230. Cited on 6, 8 and 12.Search in Google Scholar

[16] Parida, P.K. and D.K. Gupta. “Recurrence relations for a Newton-like method in Banach spaces.” J. Comput. Appl. Math. 206, no. 2 (2007): 873-887. Cited on 6, 8, 9 and 16.10.1016/j.cam.2006.08.027Search in Google Scholar

[17] Ren, Hongmin. “On the local convergence of a deformed Newton’s method under Argyros-type condition.” J. Math. Anal. Appl. 321, no. 1 (2006): 396-404. Cited on 6.10.1016/j.jmaa.2005.08.057Search in Google Scholar

[18] Rheinboldt, Werner C. “An adaptive continuation process for solving systems of nonlinear equations. vol. 3 of Banach Center Publ., 129-142. Warsaw: PWN, 1978. Cited on 6 and 12.10.4064/-3-1-129-142Search in Google Scholar

[19] Traub, J. F. Iterative methods for the solution of equations. Englewood Cliffs, N.J.: Prentice-Hall Series in Automatic Computation Prentice-Hall, Inc., 1964. Cited on 6 and 12.Search in Google Scholar

[20] Wang, Xiuhua, Jisheng Kou and Chuanqing Gu. “Semilocal convergence of a sixth-order Jarratt method in Banach spaces.” Numer. Algorithms 57, no. 4 (2011): 441-456. Cited on 6, 8 and 12.10.1007/s11075-010-9438-1Search in Google Scholar

[21] Wu, Qingbiao and Yueqing Zhao. “Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space.” Appl. Math. Comput. 175, no. 2 (2006): 1515-1524. Cited on 6.10.1016/j.amc.2005.08.043Search in Google Scholar

eISSN:
2300-133X
ISSN:
2081-545X
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
Volume Open
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines