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A family of derivative-free methods with high order of convergence and its application to nonsmooth equations

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A family of derivative-free methods with high order of convergence and its application to nonsmooth equations

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Cordero Barbero, A.; Hueso Pagoaga, JL.; Martínez Molada, E.; Torregrosa Sánchez, JR. (2012). A family of derivative-free methods with high order of convergence and its application to nonsmooth equations. Abstract and Applied Analysis. 2012:1-15. https://doi.org/10.1155/2012/836901

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/27791

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Title: A family of derivative-free methods with high order of convergence and its application to nonsmooth equations
Author: Cordero Barbero, Alicia Hueso Pagoaga, José Luís Martínez Molada, Eulalia Torregrosa Sánchez, Juan Ramón
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good ...[+]
Copyrigths: Reconocimiento (by)
Source:
Abstract and Applied Analysis. (issn: 1085-3375 )
DOI: 10.1155/2012/836901
Publisher:
Hindawi Publishing Corporation
Publisher version: http://dx.doi.org/10.1155/2012/836901
Project ID:
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
info:eu-repo/grantAgreement/UPV//PAID-06-2010-2285/
Thanks:
The authors would like to thank the referees for their valuable comments and for their suggestions to improve the readability of the paper. This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 ...[+]
Type: Artículo

References

Kung, H. T., & Traub, J. F. (1974). Optimal Order of One-Point and Multipoint Iteration. Journal of the ACM, 21(4), 643-651. doi:10.1145/321850.321860

Liu, Z., Zheng, Q., & Zhao, P. (2010). A variant of Steffensen’s method of fourth-order convergence and its applications. Applied Mathematics and Computation, 216(7), 1978-1983. doi:10.1016/j.amc.2010.03.028

Dehghan, M., & Hajarian, M. (2010). Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations. Computational & Applied Mathematics, 29(1). doi:10.1590/s1807-03022010000100002 [+]
Kung, H. T., & Traub, J. F. (1974). Optimal Order of One-Point and Multipoint Iteration. Journal of the ACM, 21(4), 643-651. doi:10.1145/321850.321860

Liu, Z., Zheng, Q., & Zhao, P. (2010). A variant of Steffensen’s method of fourth-order convergence and its applications. Applied Mathematics and Computation, 216(7), 1978-1983. doi:10.1016/j.amc.2010.03.028

Dehghan, M., & Hajarian, M. (2010). Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations. Computational & Applied Mathematics, 29(1). doi:10.1590/s1807-03022010000100002

Cordero, A., & Torregrosa, J. R. (2011). A class of Steffensen type methods with optimal order of convergence. Applied Mathematics and Computation, 217(19), 7653-7659. doi:10.1016/j.amc.2011.02.067

Amat, S., & Busquier, S. (2006). On a Steffensen’s type method and its behavior for semismooth equations. Applied Mathematics and Computation, 177(2), 819-823. doi:10.1016/j.amc.2005.11.032

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). A modified Newton-Jarratt’s composition. Numerical Algorithms, 55(1), 87-99. doi:10.1007/s11075-009-9359-z

Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062

Amat, S., & Busquier, S. (2003). On a higher order Secant method. Applied Mathematics and Computation, 141(2-3), 321-329. doi:10.1016/s0096-3003(02)00257-6

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