- -

Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods

Show full item record

Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vindel, P. (2019). Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods. Mathematical Modelling and Analysis. 24(3):335-350. https://doi.org/10.3846/mma.2019.021

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/159367

Files in this item

Item Metadata

Title: Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods
Author: Cordero Barbero, Alicia Torregrosa Sánchez, Juan Ramón Vindel, Pura
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] In this paper, we study the dynamics of an iterative method based on the Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations. As it was proven in "A new family of iterative methods widening ...[+]
Subjects: Nonlinear problems , Iterative methods , Complex dynamics , Dynamical and parameter planes , Critical points
Copyrigths: Reconocimiento (by)
Source:
Mathematical Modelling and Analysis. (issn: 1392-6292 )
DOI: 10.3846/mma.2019.021
Publisher:
Vilnius Gediminas Technical University
Publisher version: https://doi.org/10.3846/mma.2019.021
Project ID:
UJI/P1.1B20115-16
MINISTERIO DE ECONOMIA Y EMPRESA/MTM2014-52016-C2-2-P
GENERALITAT VALENCIANA/PROMETEO/2016/089
Thanks:
This research was supported by Spanish Ministry grant MTM2014-52016-C02-2-P, Generalitat Valenciana PROMETEO/2016/089 and UJI project P1.1B20115-16. The authors also want to thank the anonymous referees for their suggestions ...[+]
Type: Artículo

References

Amat, S., Busquier, S., & Plaza, S. (2007). On the dynamics of a family of third-order iterative functions. The ANZIAM Journal, 48(3), 343-359. doi:10.1017/s1446181100003539

Beardon, A. F. (Ed.). (1991). Iteration of Rational Functions. Graduate Texts in Mathematics. doi:10.1007/978-1-4612-4422-6

Blanchard, P. (1984). Complex analytic dynamics on the Riemann sphere. Bulletin of the American Mathematical Society, 11(1), 85-142. doi:10.1090/s0273-0979-1984-15240-6 [+]
Amat, S., Busquier, S., & Plaza, S. (2007). On the dynamics of a family of third-order iterative functions. The ANZIAM Journal, 48(3), 343-359. doi:10.1017/s1446181100003539

Beardon, A. F. (Ed.). (1991). Iteration of Rational Functions. Graduate Texts in Mathematics. doi:10.1007/978-1-4612-4422-6

Blanchard, P. (1984). Complex analytic dynamics on the Riemann sphere. Bulletin of the American Mathematical Society, 11(1), 85-142. doi:10.1090/s0273-0979-1984-15240-6

Budzko, D., Cordero, A., & Torregrosa, J. R. (2015). A new family of iterative methods widening areas of convergence. Applied Mathematics and Computation, 252, 405-417. doi:10.1016/j.amc.2014.12.028

Campos, B., Cordero, A., Torregrosa, J. R., & Vindel, P. (2014). Dynamics of the family of c-iterative methods. International Journal of Computer Mathematics, 92(9), 1815-1825. doi:10.1080/00207160.2014.893608

Chun, C., & Neta, B. (2018). Comparative study of methods of various orders for finding repeated roots of nonlinear equations. Journal of Computational and Applied Mathematics, 340, 11-42. doi:10.1016/j.cam.2018.02.009

Cordero, A., García-Maimó, J., Torregrosa, J. R., Vassileva, M. P., & Vindel, P. (2013). Chaos in King’s iterative family. Applied Mathematics Letters, 26(8), 842-848. doi:10.1016/j.aml.2013.03.012

Ermakov, V. V., & Kalitkin, N. N. (1981). The optimal step and regularization for Newton’s method. USSR Computational Mathematics and Mathematical Physics, 21(2), 235-242. doi:10.1016/0041-5553(81)90022-7

Gutiérrez, J. M., Hernández, M. A., & Romero, N. (2010). Dynamics of a new family of iterative processes for quadratic polynomials. Journal of Computational and Applied Mathematics, 233(10), 2688-2695. doi:10.1016/j.cam.2009.11.017

Kim, Y. I., Behl, R., & Motsa, S. S. (2017). AN OPTIMAL FAMILY OF EIGHTH-ORDER ITERATIVE METHODS WITH AN INVERSE INTERPOLATORY RATIONAL FUNCTION ERROR CORRECTOR FOR NONLINEAR EQUATIONS. Mathematical Modelling and Analysis, 22(3), 321-336. doi:10.3846/13926292.2017.1309585

Lee, M.-Y., Ik Kim, Y., & Alberto Magreñán, Á. (2017). On the dynamics of a triparametric family of optimal fourth-order multiple-zero finders with a weight function of the principal mth root of a function-to function ratio. Applied Mathematics and Computation, 315, 564-590. doi:10.1016/j.amc.2017.08.005

[-]

recommendations

 

This item appears in the following Collection(s)

Show full item record