- -

On improved three-step schemes with high efficiency index and their dynamics

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

On improved three-step schemes with high efficiency index and their dynamics

Mostrar el registro completo del ítem

Babajee, DKR.; Cordero Barbero, A.; Soleymani, F.; Torregrosa Sánchez, JR. (2014). On improved three-step schemes with high efficiency index and their dynamics. Numerical Algorithms. 65(1):153-169. https://doi.org/10.1007/s11075-013-9699-6

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/56199

Ficheros en el ítem

Thumbnail
Nombre: Cordero, A - On ...
Tamaño: 447.2Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir/Preview
[Cerrado]
Nombre: Cordero, A - On ...
Tamaño: 1.309Mb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor

Metadatos del ítem

Título: On improved three-step schemes with high efficiency index and their dynamics
Autor: Babajee, Diyashvir K. R. Cordero Barbero, Alicia Soleymani, Fazlollah Torregrosa Sánchez, Juan Ramón
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
This paper presents an improvement of the sixth-order method of Chun and Neta as a class of three-step iterations with optimal efficiency index, in the sense of Kung-Traub conjecture. Each member of the presented class ...[+]
Palabras clave: Basin of attraction , Kung-Traub conjecture , Fractal , Multi-point iterations , Julia set
Derechos de uso: Reserva de todos los derechos
Fuente:
Numerical Algorithms. (issn: 1017-1398 ) (eissn: 1572-9265 )
DOI: 10.1007/s11075-013-9699-6
Editorial:
Springer Verlag
Versión del editor: http://dx.doi.org/10.1007/s11075-013-9699-6
Código del Proyecto:
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
Agradecimientos:
This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and FONDOCYT Republica Dominicana.
Tipo: Artículo

References

Pang, J.S., Chan, D.: Iterative methods for variational and complementary problems. Math. Program. 24(1), 284–313 (1982)

Sun, D.: A class of iterative methods for solving nonlinear projection equations. J. Optim. Theory Appl. 91(1), 123–140 (1996)

Chun, C., Neta, B.: A new sixth-order scheme for nonlinear equations. Appl. Math. Lett. 25, 185–189 (2012) [+]
Pang, J.S., Chan, D.: Iterative methods for variational and complementary problems. Math. Program. 24(1), 284–313 (1982)

Sun, D.: A class of iterative methods for solving nonlinear projection equations. J. Optim. Theory Appl. 91(1), 123–140 (1996)

Chun, C., Neta, B.: A new sixth-order scheme for nonlinear equations. Appl. Math. Lett. 25, 185–189 (2012)

Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. ACM 21, 643–651 (1974)

Neta, B.: A new family of high-order methods for solving equations. Int. J. Comput. Math. 14, 191–195 (1983)

Neta, B.: On Popovski’s method for nonlinear equations. Appl. Math. Comput. 201, 710–715 (2008)

Chun, C., Neta, B.: Some modifications of Newton’s method by the method of undeterminate coefficients. Comput. Math. Appl. 56, 2528–2538 (2008)

Chun, C., Lee, M.Y., Neta, B., Dzunic, J.: On optimal fourth-order iterative methods free from second derivative and their dynamics. Appl. Math. Comput. 218, 6427–6438 (2012)

Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Three-step iterative methods with optimal eighth-order convergence. J. Comput. Appl. Math. 235, 3189–3194 (2011)

Cordero, A., Torregrosa, J.R., Vassileva, M.P.: A family of modified Ostrowski’s methods with optimal eighth order of convergence. Appl. Math. Lett. 24, 2082–2086 (2011)

Heydari, M., Hosseini, S.M., Loghmani, G.B.: On two new families of iterative methods for solving nonlinear equations with optimal order. Appl. Anal. Dis. Math. 5, 93–109 (2011)

Neta, B., Petkovic, M.S.: Construction of optimal order nonlinear solvers using inverse interpolation. Appl. Math. Comput. 217, 2448–2445 (2010)

Sharifi, M., Babajee, D.K.R., Soleymani, F.: Finding the solution of nonlinear equations by a class of optimal methods. Comput. Math. Appl. 63, 764–774 (2012)

Soleymani, F., Karimi Vanani, S., Khan, M., Sharifi, M.: Some modifications of King’s family with optimal eighth order of convergence. Math. Comput. Model. 55, 1373–1380 (2012)

Soleymani, F., Karimi Vanani, S., Jamali Paghaleh, M.: A class of three-step derivative-free root solvers with optimal convergence order. J. Appl. Math. 2012, Article ID 568740, 15 pp. (2012). doi: 10.1155/2012/568740

Soleymani, F., Sharifi, M., Mousavi, B.S.: An improvement of Ostrowski’s and King’s techniques with optimal convergence order eight. J. Optim. Theory Appl. 153, 225–236 (2012)

Stewart, B.D.: Attractor basins of various root-finding methods. M.S. Thesis, Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA (2001)

Amat, S., Busquier, S., Plaza, S.: Review of some iterative root-finding methods from a dynamical point of view. Scientia 10, 3–35 (2004)

Amat, S., Busquier, S., Plaza, S.: Dynamics of the King and Jarratt iterations. Aequ. Math. 69, 212–223 (2005)

Amat, S., Busquier, S., Plaza, S.: Chaotic dynamics of a third-order Newton type method. J. Math. Anal. Appl. 366, 24–32 (2010)

Neta, B., Chun, C., Scott, M.: A note on the modified super-Halley method. Appl. Math. Comput. 218, 9575–9577 (2012)

Scott, M., Neta, B., Chun, C.: Basin attractors for various methods. Appl. Math. Comput. 218, 2584–2599 (2011)

Ardelean, G.: A comparison between iterative methods by using the basins of attraction. Appl. Math. Comput. 218, 88–95 (2011)

Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice Hall, New York (1964)

Babajee, D.K.R.: Analysis of higher order variants of Newton’s method and their applications to differential and integral equations and in ocean acidification. Ph.D. Thesis, University of Mauritius (2010)

[-]

recommendations

 

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

Mostrar el registro completo del ítem