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Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions

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Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions

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Zafar, F.; Cordero Barbero, A.; Junjua, M.; Torregrosa Sánchez, JR. (2020). Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-17. https://doi.org/10.1007/s13398-020-00794-7

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Título: Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions
Autor: Zafar, Fiza Cordero Barbero, Alicia Junjua, Moin-ud-Din Torregrosa Sánchez, Juan Ramón
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] It is well known that the optimal iterative methods are of more significance than the non-optimal ones in view of their efficiency and convergence speed. There are only a few number of optimal iterative methods for ...[+]
Palabras clave: Nonlinear equations , Order of convergence , Multiple roots , Optimality
Derechos de uso: Cerrado
Fuente:
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. (issn: 1578-7303 )
DOI: 10.1007/s13398-020-00794-7
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s13398-020-00794-7
Código del Proyecto:
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/
Agradecimientos:
This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), Generalitat Valenciana PROMETEO/2016/089 and Schlumberger Foundation-Faculty for Future Program.
Tipo: Artículo

References

Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R.: On developing fourth-order optimal families of methods for multiple roots and their dynamics. Appl. Math. Comput. 265(15), 520–532 (2015)

Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R.: An eighth-order family of optimal multiple root finders and its dynamics. Numer. Algorithm (2017). https://doi.org/10.1007/s11075-017-0361-6

Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R., Kanwar, V.: An optimal fourth-order family of methods for multiple roots and its dynamics. Numer. Algorithm 71(4), 775–796 (2016) [+]
Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R.: On developing fourth-order optimal families of methods for multiple roots and their dynamics. Appl. Math. Comput. 265(15), 520–532 (2015)

Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R.: An eighth-order family of optimal multiple root finders and its dynamics. Numer. Algorithm (2017). https://doi.org/10.1007/s11075-017-0361-6

Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R., Kanwar, V.: An optimal fourth-order family of methods for multiple roots and its dynamics. Numer. Algorithm 71(4), 775–796 (2016)

Chicharro, F.I., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameters planes of iterative families and methods. Sci. World J. (2013) (Article ID 780153, 9 pages)

Geum, Y.H., Kim, Y.I., Neta, B.: A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics. Appl. Math. Comput. 270, 387–400 (2015)

Geum, Y.H., Kim, Y.I., Neta, B.: A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Appl. Math. Comput. 283, 120–140 (2016)

Geum, Y.H., Kim, Y.I., Neta, B.: Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with dynamics be-hind their purely imaginary extraneous fixed points. J. Comput. Appl. Math. 333, 131–156 (2018)

Hueso, J.L., Martínez, E., Teruel, C.: Determination of multiple roots of nonlinear equations and applications. J. Math. Chem. 53, 880–892 (2015)

Jay, L.O.: A note on Q-order of convergence. BIT Numer. Math. 41, 422–429 (2001)

Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. Assoc. Comput. Mach. 21, 643–651 (1974)

Li, S.G., Cheng, L.Z., Neta, B.: Some fourth-order nonlinear solvers with closed formulae for multiple roots. Comput. Math. Appl. 59, 126–135 (2010)

Li, S., Liao, X., Cheng, L.: A new fourth-order iterative method for finding multiple roots of nonlinear equations. Appl. Math. Comput. 215, 1288–1292 (2009)

Liu, B., Zhou, X.: A new family of fourth-order methods for multiple roots of nonlinear equations. Nonlinear Anal. Model. Control 18(2), 143–152 (2013)

Neta, B.: Extension of Murakami’s high-order non-linear solver to multiple roots. Int. J. Comput. Math. 87(5), 1023–1031 (2010)

Ostrowski, A.M.: Solution of Equations and Systems of Equations. Academic Press, New York (1960)

Petković, M.S., Neta, B., Petković, L.D., Dz̆unić, J.: Multipoint Methods for Solving Nonlinear Equations. Academic Press, New York (2013)

Shacham, M.: Numerical solution of constrained nonlinear algebraic equations. Int. J. Numer. Method Eng. 23, 1455–1481 (1986)

Sharifi, M., Babajee, D.K.R., Soleymani, F.: Finding the solution of nonlinear equations by a class of optimal methods. Comput. Math. Appl. 63, 764–774 (2012)

Sharma, J.R., Sharma, R.: Modified Jarratt method for computing multiple roots. Appl. Math. Comput. 217, 878–881 (2010)

Soleymani, F., Babajee, D.K.R.: Computing multiple zeros using a class of quartically convergent methods. Alex. Eng. J. 52, 531–541 (2013)

Soleymani, F., Babajee, D.K.R., Lofti, T.: On a numerical technique for finding multiple zeros and its dynamic. Egypt. Math. Soc. 21, 346–353 (2013)

Thukral, R.: Introduction to higher-order iterative methods for finding multiple roots of nonlinear equations. J. Math. (2013). https://doi.org/10.1155/2013/404635. (Article ID 404635, 3 pages)

Thukral, R.: A new family of fourth-order iterative methods for solving nonlinear equations with multiple roots. Numer. Math. Stoch. 6(1), 37–44 (2014)

Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs (1964)

Zafar, F., Cordero, A., Quratulain, R., Torregrosa, J.R.: Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters. J. Math. Chem. (2017). https://doi.org/10.1007/s10910-017-0813-1

Zhou, X., Chen, X., Song, Y.: Constructing higher-order methods for obtaining the muliplte roots of nonlinear equations. Comput. Math. Appl. 235, 4199–4206 (2011)

Zhou, X., Chen, X., Song, Y.: Families of third and fourth order methods for multiple roots of nonlinear equations. Appl. Math. Comput. 219, 6030–6038 (2013)

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