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Anomalies in the convergence of Traub-type methods with memory

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Anomalies in the convergence of Traub-type methods with memory

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Chicharro, FI.; Cordero Barbero, A.; Garrido, N.; Torregrosa Sánchez, JR. (2020). Anomalies in the convergence of Traub-type methods with memory. Computational and Mathematical Methods. 2(1):1-13. https://doi.org/10.1002/cmm4.1060

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/163182

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Metadatos del ítem

Título: Anomalies in the convergence of Traub-type methods with memory
Autor: Chicharro, Francisco I. Cordero Barbero, Alicia Garrido, Neus Torregrosa Sánchez, Juan Ramón
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària
Fecha difusión:
Resumen:
[EN] The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the ...[+]
Palabras clave: Basin of attraction , Fixed points , Iterative processes with memory , Nonlinear equation
Derechos de uso: Cerrado
Fuente:
Computational and Mathematical Methods. (eissn: 2577-7408 )
DOI: 10.1002/cmm4.1060
Editorial:
John Wiley & Sons
Versión del editor: https://doi.org/10.1002/cmm4.1060
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 the Ministerio de Ciencia, Innovación y Universidades (Spain) (PGC2018-095896-B-C22) and Generalitat Valenciana (PROMETEO/2016/089). In addition, the authors would like to thank ...[+]
Tipo: 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

Petković, M. S., & Sharma, J. R. (2015). On some efficient derivative-free iterative methods with memory for solving systems of nonlinear equations. Numerical Algorithms, 71(2), 457-474. doi:10.1007/s11075-015-0003-9

Chun, C., & Neta, B. (2017). How good are methods with memory for the solution of nonlinear equations? SeMA Journal, 74(4), 613-625. doi:10.1007/s40324-016-0105-x [+]
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

Petković, M. S., & Sharma, J. R. (2015). On some efficient derivative-free iterative methods with memory for solving systems of nonlinear equations. Numerical Algorithms, 71(2), 457-474. doi:10.1007/s11075-015-0003-9

Chun, C., & Neta, B. (2017). How good are methods with memory for the solution of nonlinear equations? SeMA Journal, 74(4), 613-625. doi:10.1007/s40324-016-0105-x

Soleymani, F. (2013). Some optimal iterative methods and their with memory variants. Journal of the Egyptian Mathematical Society, 21(2), 133-141. doi:10.1016/j.joems.2013.01.002

Zafar, F., Akram, S., Yasmin, N., & Junjua, M.-D. (2016). On the construction of three step derivative free four-parametric methods with accelerated order of convergence. Journal of Nonlinear Sciences and Applications, 09(06), 4542-4553. doi:10.22436/jnsa.009.06.92

Cordero, A., Junjua, M.-D., Torregrosa, J. R., Yasmin, N., & Zafar, F. (2018). Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices. Mathematical Problems in Engineering, 2018, 1-12. doi:10.1155/2018/8093673

Lotfi, T., Soleymani, F., Ghorbanzadeh, M., & Assari, P. (2015). On the construction of some tri-parametric iterative methods with memory. Numerical Algorithms, 70(4), 835-845. doi:10.1007/s11075-015-9976-7

Sharma, J. R., & Arora, H. (2017). Efficient higher order derivative-free multipoint methods with and without memory for systems of nonlinear equations. International Journal of Computer Mathematics, 95(5), 920-938. doi:10.1080/00207160.2017.1298747

Campos, B., Cordero, A., Torregrosa, J. R., & Vindel, P. (2017). Stability of King’s family of iterative methods with memory. Journal of Computational and Applied Mathematics, 318, 504-514. doi:10.1016/j.cam.2016.01.035

Chicharro, F. I., Cordero, A., & Torregrosa, J. R. (2019). Dynamics of iterative families with memory based on weight functions procedure. Journal of Computational and Applied Mathematics, 354, 286-298. doi:10.1016/j.cam.2018.01.019

Chicharro, F. I., Cordero, A., Garrido, N., & Torregrosa, J. R. (2018). Stability and applicability of iterative methods with memory. Journal of Mathematical Chemistry, 57(5), 1282-1300. doi:10.1007/s10910-018-0952-z

Chicharro, F. I., Cordero, A., & Torregrosa, J. R. (2013). Drawing Dynamical and Parameters Planes of Iterative Families and Methods. The Scientific World Journal, 2013, 1-11. doi:10.1155/2013/780153

Varona, J. L. (2002). Graphic and numerical comparison between iterative methods. The Mathematical Intelligencer, 24(1), 37-46. doi:10.1007/bf03025310

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