- -

Impact on stability by the use of memory in Traub-type schemes

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Impact on stability by the use of memory in Traub-type schemes

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Chicharro;Cordero ...
Tamaño: 5.434Mb
Formato: PDF
Descripción: Versión editorial
Abrir
dc.contributor.author Chicharro, Francisco I. es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Garrido, Neus es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2021-02-24T04:31:59Z
dc.date.available 2021-02-24T04:31:59Z
dc.date.issued 2020-02 es_ES
dc.identifier.uri http://hdl.handle.net/10251/162251
dc.description.abstract [EN] In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub's method, they have been designed using linear approximations or the Newton's interpolation polynomials. In both cases, the parameters use information from the current and the previous iterations, so they define a method with memory. Moreover, they achieve higher order of convergence than Traub's scheme without any additional functional evaluations. The real dynamical analysis verifies that the proposed methods with memory not only converge faster, but they are also more stable than the original scheme. The methods selected by means of this analysis can be applied for solving nonlinear problems with a wider set of initial estimations than their original partners. This fact also involves a lower number of iterations in the process. es_ES
dc.description.sponsorship This research was partially supported by Ministerio de Ciencia, Innovacion y Universidades under grants PGC2018-095896-B-C22 (MCIU/AEI/FEDER/UE). es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Nonlinear dynamics es_ES
dc.subject Iterative methods with memory es_ES
dc.subject Multidimensional dynamics es_ES
dc.subject Accelerator parameter es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Impact on stability by the use of memory in Traub-type schemes es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math8020274 es_ES
dc.relation.projectID 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/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària es_ES
dc.description.bibliographicCitation Chicharro, FI.; Cordero Barbero, A.; Garrido, N.; Torregrosa Sánchez, JR. (2020). Impact on stability by the use of memory in Traub-type schemes. Mathematics. 8(2):1-16. https://doi.org/10.3390/math8020274 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math8020274 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 16 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 8 es_ES
dc.description.issue 2 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\423831 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.description.references Shacham, M. (1989). An improved memory method for the solution of a nonlinear equation. Chemical Engineering Science, 44(7), 1495-1501. doi:10.1016/0009-2509(89)80026-0 es_ES
dc.description.references Balaji, G. V., & Seader, J. D. (1995). Application of interval Newton’s method to chemical engineering problems. Reliable Computing, 1(3), 215-223. doi:10.1007/bf02385253 es_ES
dc.description.references Shacham, M. (1986). Numerical solution of constrained non-linear algebraic equations. International Journal for Numerical Methods in Engineering, 23(8), 1455-1481. doi:10.1002/nme.1620230805 es_ES
dc.description.references Shacham, M., & Kehat, E. (1973). Converging interval methods for the iterative solution of a non-linear equation. Chemical Engineering Science, 28(12), 2187-2193. doi:10.1016/0009-2509(73)85008-0 es_ES
dc.description.references Amat, S., Busquier, S., & Plaza, S. (2010). Chaotic dynamics of a third-order Newton-type method. Journal of Mathematical Analysis and Applications, 366(1), 24-32. doi:10.1016/j.jmaa.2010.01.047 es_ES
dc.description.references Argyros, I. K., Cordero, A., Magreñán, Á. A., & Torregrosa, J. R. (2017). Third-degree anomalies of Traub’s method. Journal of Computational and Applied Mathematics, 309, 511-521. doi:10.1016/j.cam.2016.01.060 es_ES
dc.description.references Chicharro, F., Cordero, A., Gutiérrez, J. M., & Torregrosa, J. R. (2013). Complex dynamics of derivative-free methods for nonlinear equations. Applied Mathematics and Computation, 219(12), 7023-7035. doi:10.1016/j.amc.2012.12.075 es_ES
dc.description.references Chicharro, F., Cordero, A., & Torregrosa, J. (2015). Dynamics and Fractal Dimension of Steffensen-Type Methods. Algorithms, 8(2), 271-279. doi:10.3390/a8020271 es_ES
dc.description.references Scott, M., Neta, B., & Chun, C. (2011). Basin attractors for various methods. Applied Mathematics and Computation, 218(6), 2584-2599. doi:10.1016/j.amc.2011.07.076 es_ES
dc.description.references Steffensen, J. F. (1933). Remarks on iteration. Scandinavian Actuarial Journal, 1933(1), 64-72. doi:10.1080/03461238.1933.10419209 es_ES
dc.description.references Wang, X., & Zhang, T. (2012). A new family of Newton-type iterative methods with and without memory for solving nonlinear equations. Calcolo, 51(1), 1-15. doi:10.1007/s10092-012-0072-2 es_ES
dc.description.references Džunić, J., & Petković, M. S. (2014). On generalized biparametric multipoint root finding methods with memory. Journal of Computational and Applied Mathematics, 255, 362-375. doi:10.1016/j.cam.2013.05.013 es_ES
dc.description.references Petković, M. S., Neta, B., Petković, L. D., & Džunić, J. (2014). Multipoint methods for solving nonlinear equations: A survey. Applied Mathematics and Computation, 226, 635-660. doi:10.1016/j.amc.2013.10.072 es_ES
dc.description.references Campos, B., Cordero, A., Torregrosa, J. R., & Vindel, P. (2015). A multidimensional dynamical approach to iterative methods with memory. Applied Mathematics and Computation, 271, 701-715. doi:10.1016/j.amc.2015.09.056 es_ES
dc.description.references 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 es_ES
dc.description.references Chicharro, F. I., Cordero, A., Torregrosa, J. R., & Vassileva, M. P. (2017). King-Type Derivative-Free Iterative Families: Real and Memory Dynamics. Complexity, 2017, 1-15. doi:10.1155/2017/2713145 es_ES
dc.description.references Magreñán, Á. A., Cordero, A., Gutiérrez, J. M., & Torregrosa, J. R. (2014). Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane. Mathematics and Computers in Simulation, 105, 49-61. doi:10.1016/j.matcom.2014.04.006 es_ES
dc.description.references Blanchard, P. (1984). Complex analytic dynamics on the Riemann sphere. Bulletin of the American Mathematical Society, 11(1), 85-141. doi:10.1090/s0273-0979-1984-15240-6 es_ES
dc.description.references Magreñán, Á. A. (2014). A new tool to study real dynamics: The convergence plane. Applied Mathematics and Computation, 248, 215-224. doi:10.1016/j.amc.2014.09.061 es_ES
dc.description.references 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 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem