Mostrar el registro sencillo del ítem
dc.contributor.author | Kansal, Munish | es_ES |
dc.contributor.author | Cordero Barbero, Alicia | es_ES |
dc.contributor.author | Bhalla, Sonia | es_ES |
dc.contributor.author | Torregrosa Sánchez, Juan Ramón | es_ES |
dc.date.accessioned | 2022-04-05T06:28:48Z | |
dc.date.available | 2022-04-05T06:28:48Z | |
dc.date.issued | 2021-07 | es_ES |
dc.identifier.issn | 1017-1398 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/181767 | |
dc.description.abstract | [EN] In this paper, a two-step class of fourth-order iterative methods for solving systems of nonlinear equations is presented. We further extend the two-step class to establish a new sixth-order family which requires only one additional functional evaluation. The convergence analysis of the proposed classes is provided under several mild conditions. A complete dynamical analysis is made, by using real multidimensional discrete dynamics, in order to select the most stable elements of both families of fourth- and sixth-order of convergence. To get this aim, a novel tool based on the existence of critical points has been used, the parameter line. The analytical discussion of the work is upheld by performing numerical experiments on some application-oriented problems. We provide an implementation of the proposed scheme on nonlinear optimization problem and zero-residual nonlinear least-squares problems taken from the constrained and unconstrained testing environment test set. Finally, based on numerical results, it has been concluded that our methods are comparable with the existing ones of similar nature in terms of order, efficiency, and computational time and also that the stability results provide the most efficient member of each class of iterative schemes. | es_ES |
dc.description.sponsorship | This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), Generalitat Valenciana PROMETEO/2016/089 | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Springer-Verlag | es_ES |
dc.relation.ispartof | Numerical Algorithms | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Systems of nonlinear equations | es_ES |
dc.subject | Order of convergence | es_ES |
dc.subject | Multipoint iterative methods | es_ES |
dc.subject | Stability analysis | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | New fourth and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1007/s11075-020-00997-4 | 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.relation.projectID | info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//PROMETEO%2F2016%2F089//RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES MEDIANTE TECNICAS ITERATIVAS: ANALISIS DINAMICO Y APLICACIONES/ | 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.description.bibliographicCitation | Kansal, M.; Cordero Barbero, A.; Bhalla, S.; Torregrosa Sánchez, JR. (2021). New fourth and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis. Numerical Algorithms. 87(3):1017-1060. https://doi.org/10.1007/s11075-020-00997-4 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1007/s11075-020-00997-4 | es_ES |
dc.description.upvformatpinicio | 1017 | es_ES |
dc.description.upvformatpfin | 1060 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 87 | es_ES |
dc.description.issue | 3 | es_ES |
dc.relation.pasarela | S\423918 | es_ES |
dc.contributor.funder | GENERALITAT VALENCIANA | es_ES |
dc.contributor.funder | AGENCIA ESTATAL DE INVESTIGACION | es_ES |
dc.contributor.funder | European Regional Development Fund | es_ES |
dc.description.references | Cordero, A., Torregrosa, J. R.: Variants of Newton’s method for functions of several variables. Appl. Math. Comput. 183, 199–208 (2006) | es_ES |
dc.description.references | Frontini, M., Sormani, E.: Third-order methods from quadrature formulae for solving systems of nonlinear equations. Appl. Math. Comput. 149, 771–782 (2004) | es_ES |
dc.description.references | Grau-Sánchez, M., Grau, À., Noguera, M.: On the computational efficiency index and some iterative methods for solving systems of non-linear equations. Comput. Appl. Math. 236, 1259–1266 (2011) | es_ES |
dc.description.references | Homeier, H. H. H.: A modified Newton method with cubic convergence:the multivariable case. Comput Appl. Math. 169, 161–169 (2004) | es_ES |
dc.description.references | Cordero, A., Torregrosa, J. R.: Variants of Newton’s method using fifth-order quadrature formulas. Comput. Appl. Math. 190, 686–698 (2007) | es_ES |
dc.description.references | Darvishi, M. T., Barati, A.: Super cubic iterative methods to solve systems of nonlinear equations. Appl. Math. Comput. 188, 1678–1685 (2007) | es_ES |
dc.description.references | Darvishi, M. T., Barati, A.: A third-order Newton-type method to solve systems of non-linear equations. Appl.Math. Comput. 187, 630–635 (2007) | es_ES |
dc.description.references | Potra, F. A., Pták, V.: Nondiscrete Induction and Iterarive Processes Pitman Publishing Boston (1984) | es_ES |
dc.description.references | Babajee, D. K. R., Madhu, K., Jayaraman, J.: On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations. Algor. 8, 895–909 (2015) | es_ES |
dc.description.references | Cordero, A., Torregrosa, J.R.: Iterative methods of order four and five for systems of nonlinear equations. Comput. Appl. Math. 231, 541–551 (2009) | es_ES |
dc.description.references | Cordero, A., Hueso, J. L., Martínez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Appl. Math. Comput. 217, 4548–4556 (2011) | es_ES |
dc.description.references | Arroyo, V., Cordero, A., Torregrosa, J. R.: Approximation of artificial satellites’ preliminary orbits: the efficiency challenge. Math. Comput. Modelling 54, 1802–1807 (2011) | es_ES |
dc.description.references | Cordero, A., Torregrosa, J. R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007) | es_ES |
dc.description.references | Narang, M., Bhatia, S., Kanwar, V.: New two-parameter Chebyshev Halley-like family of fourth and sixth-order methods for systems of nonlinear equations. Appl. Math. Comput. 275, 394–403 (2016) | es_ES |
dc.description.references | Lotfi, T., Bakhtiari, P., Cordero, A., Mahdiani, K., Torregrosa, J. R.: Some new efficient multipoint iterative methods for solving nonlinear systems of equations. Int. J. Comput. Math. 92, 1921–1934 (2015) | es_ES |
dc.description.references | Alzahrani, A. K. H., Behl, R., Alshomrani, A.: Some higher-order iteration functions for solving nonlinear models. Appl. Math. Comput. 334, 80–93 (2018) | es_ES |
dc.description.references | Babajee, D. K. R.: On a two-parameter Chebyshev-Halley like family of optimal two-point fourth order methods free from second derivatives. Afrika Matematika. 26, 689–695 (2015) | es_ES |
dc.description.references | Behl, R., Kanwar, V.: Highly efficient classes of Chebyshev-Halley type methods free from second-order derivative (2014) | es_ES |
dc.description.references | Ortega, J. M., Rheinboldt, W. C.: Iterative Solution of Nonlinear Equations in Several Variables Academic Press New York (1970) | es_ES |
dc.description.references | Cordero, A., Hueso, J. L., Torregrosa, J.R.: A modified Newton-Jarratt’s composition. Numer. Algor. 55, 87–99 (2010) | es_ES |
dc.description.references | Fatou, P.: Sur les équations fonctionelles. Bull. Soc. Mat. Fr. 47 (1919) 161–271 48, 33–94 (1920) | es_ES |
dc.description.references | Julia, G.: Mémoire sur l’iteration des fonctions rationnelles. J. Mat. Pur. Appl. 8, 47–245 (1918) | es_ES |
dc.description.references | Chicharro, F.I., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameters planes of iterative families and methods, The Scientific World Journal, Volume 2013, Article ID 780153, 11 pages | es_ES |
dc.description.references | Cordero, A., García, J., Torregrosa, J.R., Vassileva, M.P., Vindel, P.: Chaos in King’s iterative family. Appl. Math. Letters 26, 842–848 (2013) | es_ES |
dc.description.references | Amat, S., Busquier, S., Bermúdez, C., Plaza, S.: On two families of high order Newton type methods. Appl. Math. Letters 25, 2209–2217 (2012) | es_ES |
dc.description.references | Neta, B., Chun, C., Scott, M.: Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations. Appl. Math. Comput. 227, 567–592 (2014) | es_ES |
dc.description.references | Amat, S., Busquier, S., Plaza, S.: Chaotic dynamics of a third-order Newton-type method. J. Math. Anal. Appl. 366, 24–32 (2010) | es_ES |
dc.description.references | Cordero, A., Torregrosa, J. R., Vindel, P.: Dynamics of a family of Chebyshev-Halley type methods. Appl. Math. Comput. 219, 8568–8583 (2013) | es_ES |
dc.description.references | Geum, Y. H., Kim, Y. I., Neta, B.: A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Appl. Math. Comput. 283, 120–140 (2016) | es_ES |
dc.description.references | Cordero, A., Giménez-Palacios, I., Torregrosa, J. R.: Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems. Appl. Num. Math. 137, 1–18 (2019) | es_ES |
dc.description.references | Cordero, A., Soleymani, F., Torregrosa, J. R.: Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?. Appl. Math. Comput. 244, 398–412 (2014) | es_ES |
dc.description.references | Chicharro, F.I., Cordero, A., Torregrosa, J.T.: Real stability of an efficient family of iterative methods for solving nonlinear systems. In: Proceedings of XXV Congreso de ecuaciones diferenciales y aplicaciones CEDYA 2017, ISBN 978-84-944402-1-2, 206–212 Chicharro, F.I., Cordero, A., Torregrosa, J.T.: Real stability of an efficient family of iterative methods for solving nonlinear systems. Proceedings of XXV Congreso de ecuaciones diferenciales y aplicaciones CEDYA 2017, ISBN 978-84-944402-1-2, 206–212 (2017) | es_ES |
dc.description.references | Robinson, R. C.: An introduction to dynamical systems, continous and discrete, americal mathematical society, providence, RI USA (2012) | es_ES |
dc.description.references | Devaney, R. L.: An Introduction to Chaotic Dynamical Systems Advances in Mathematics and Engineering CRC Press (2003) | es_ES |
dc.description.references | Sharma, J. R., Arora, H.: Efficient Jarratt-like methods for solving systems of nonlinear equations. Calcolo 51, 193–210 (2014) | es_ES |
dc.description.references | Jarratt, P.: Some fourth order multipoint iterative methods for solving equations. Math. Comput. 20, 434–437 (1966) | es_ES |
dc.description.references | Hillstrom, K.E.: A stmulatlon test approach to the evaluation of nonlinear optimization algorithms. ACM Trans. Math Softw. 3(4), 305–315 (1977) | es_ES |
dc.description.references | Box, M.J.: A comparison of several current optimization methods, and the use of transformations in constrained problems. Comput. J 9, 67–77 (1966) | es_ES |
dc.description.references | Recktenwald, G.: Least squares fitting of data to a curve, department of mechanical engineering portland state university (2001) | es_ES |
dc.description.references | Argyros, I.K., Hilout, S.: Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications, World Scientific Publications (2013) | es_ES |
dc.description.references | Kamenetskii, F., Al’bertovich, D.: Diffusion and heat transfer in chemical kinetics Plenum Press (1969) | es_ES |
dc.description.references | Alaidarous, E. S., Ullah, M. Z., Ahmad, F., Al-Fhaid, A. S.: An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs J Appl Math Hindawi pulisher (2013) | es_ES |
dc.description.references | Dolan, E. D., Moŕe, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002) | es_ES |