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Stability analysis of Jacobian-free Newton's iterative method

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Stability analysis of Jacobian-free Newton's iterative method

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Amiri, A.; Cordero Barbero, A.; Darvishi, M.; Torregrosa Sánchez, JR. (2019). Stability analysis of Jacobian-free Newton's iterative method. Algorithms. 12(11):1-16. https://doi.org/10.3390/a12110236

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/142897

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Title: Stability analysis of Jacobian-free Newton's iterative method
Author: Amiri, Abdolreza Cordero Barbero, Alicia Darvishi, M.T. Torregrosa Sánchez, Juan Ramón
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial ...[+]
Subjects: Nonlinear system of equations , Iterative method , Jacobian-free scheme , Basin of attraction
Copyrigths: Reconocimiento (by)
Source:
Algorithms. (eissn: 1999-4893 )
DOI: 10.3390/a12110236
Publisher:
MDPI AG
Publisher version: https://doi.org/10.3390/a12110236
Project ID:
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/
Thanks:
This research was partially supported by Spanish Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and Generalitat Valenciana PROMETEO/2016/089.
Type: Artículo

References

Grau-Sánchez, M., Noguera, M., & Amat, S. (2013). On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods. Journal of Computational and Applied Mathematics, 237(1), 363-372. doi:10.1016/j.cam.2012.06.005

Amiri, A. R., Cordero, A., Darvishi, M. T., & Torregrosa, J. R. (2018). Preserving the order of convergence: Low-complexity Jacobian-free iterative schemes for solving nonlinear systems. Journal of Computational and Applied Mathematics, 337, 87-97. doi:10.1016/j.cam.2018.01.004

Amiri, A. R., Cordero, A., Darvishi, M. T., & Torregrosa, J. R. (2018). Stability analysis of Jacobian-free iterative methods for solving nonlinear systems by using families of mth power divided differences. Journal of Mathematical Chemistry, 57(5), 1344-1373. doi:10.1007/s10910-018-0971-9 [+]
Grau-Sánchez, M., Noguera, M., & Amat, S. (2013). On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods. Journal of Computational and Applied Mathematics, 237(1), 363-372. doi:10.1016/j.cam.2012.06.005

Amiri, A. R., Cordero, A., Darvishi, M. T., & Torregrosa, J. R. (2018). Preserving the order of convergence: Low-complexity Jacobian-free iterative schemes for solving nonlinear systems. Journal of Computational and Applied Mathematics, 337, 87-97. doi:10.1016/j.cam.2018.01.004

Amiri, A. R., Cordero, A., Darvishi, M. T., & Torregrosa, J. R. (2018). Stability analysis of Jacobian-free iterative methods for solving nonlinear systems by using families of mth power divided differences. Journal of Mathematical Chemistry, 57(5), 1344-1373. doi:10.1007/s10910-018-0971-9

Neta, B., Chun, C., & Scott, M. (2014). Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations. Applied Mathematics and Computation, 227, 567-592. doi:10.1016/j.amc.2013.11.017

Geum, Y. H., Kim, Y. I., & Neta, B. (2015). A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics. Applied Mathematics and Computation, 270, 387-400. doi:10.1016/j.amc.2015.08.039

Cordero, A., Soleymani, F., & Torregrosa, J. R. (2014). Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension? Applied Mathematics and Computation, 244, 398-412. doi:10.1016/j.amc.2014.07.010

Cordero, A., Maimó, J. G., Torregrosa, J. R., & Vassileva, M. P. (2017). Multidimensional stability analysis of a family of biparametric iterative methods: CMMSE2016. Journal of Mathematical Chemistry, 55(7), 1461-1480. doi:10.1007/s10910-016-0724-6

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

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