- -

Two optimal general classes of iterative methods with eighth-order

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

  • Estadisticas de Uso

Two optimal general classes of iterative methods with eighth-order

Show full item record

Cordero Barbero, A.; Lotfi, T.; Mahdiani, K.; Torregrosa Sánchez, JR. (2014). Two optimal general classes of iterative methods with eighth-order. Acta Applicandae Mathematicae. 134(1):61-74. https://doi.org/10.1007/s10440-014-9869-0

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/54768

Files in this item

Item Metadata

Title: Two optimal general classes of iterative methods with eighth-order
Author: Cordero Barbero, Alicia Lotfi, Taher Mahdiani, Katayoun Torregrosa Sánchez, Juan Ramón
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
Two new three-step classes of optimal iterative methods to approximate simple roots of nonlinear equations, satisfying the Kung-Traub's conjecture, are designed. The development of the methods and their convergence analysis ...[+]
Subjects: Multipoint iterative method , Nonlinear equation , Optimal order , Kung-Traub's conjecture , Kung-Traub's method
Copyrigths: Cerrado
Source:
Acta Applicandae Mathematicae. (issn: 0167-8019 )
DOI: 10.1007/s10440-014-9869-0
Publisher:
Springer Verlag (Germany)
Publisher version: http://dx.doi.org/10.1007/s10440-014-9869-0
Project ID:
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
Thanks:
This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02.
Type: Artículo

References

Higham, N.J.: Funstions of Matrices: Theory and Computation. SIAM, Philadelphia (2008)

Chun, C., Kim, Y.: Several new third-order iterative methods for solving nonlinear equations. Acta Appl. Math. 109(3), 1053–1063 (2010)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007) [+]
Higham, N.J.: Funstions of Matrices: Theory and Computation. SIAM, Philadelphia (2008)

Chun, C., Kim, Y.: Several new third-order iterative methods for solving nonlinear equations. Acta Appl. Math. 109(3), 1053–1063 (2010)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007)

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: A family of iterative methods with sixth and seventh order convergence for nonlinear equations. Math. Comput. Model. 52, 1490–1496 (2010)

Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(8), 87–93 (2000)

Wang, H., Liu, H.: Note on a cubically convergent Newton-type method under weak conditions. Acta Appl. Math. 110(2), 725–735 (2010)

Ostrowski, A.M.: Solution of Equations and Systems of Equations. Prentice-Hall, Englewood Cliffs (1964)

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

Petković, M.S., Neta, B., Petković, L.D., Dz̆nić, J.: Multipoint Methods for Solving Nonlinear Equations. Elsevier, Amsterdam (2013)

Petković, M.S., Petković, L.D.: Families of optimal multipoint methods for solving polynomial equations. Appl. Anal. Discrete Math. 4, 1–22 (2010)

Soleymani, F.: Two novel classes of two-step optimal methods for all the zeros in an interval. Afr. Math. (2012). doi: 10.1007/s13370-012-0112-8

Džunić, J., Petković, M.S., Petković, L.D.: A family of optimal three-point methods for solving nonlinear equations using two parametric functions. Appl. Math. Comput. 217(19), 7612–7619 (2011)

Thukral, R., Petković, M.S.: A family of three-point methods of optimal order for solving nonlinear equation. J. Comput. Appl. Math. 233(9), 2278–2284 (2010)

Obrechkoff, N.: Sur la solution numeriue des equations. God. Sofij. Univ. 56(1), 73–83 (1963)

Jarratt, P.: Some fourth order multipoint iterative methods for solving equations. Math. Comput. 20, 434–437 (1966)

Petković, M.S.: Multipoint methods for solving nonlinear equations: a survey. Appl. Math. Comput. 226, 635–660 (2014)

Džunić, J., Petković, M.S.: A family of three-point methods of Ostrowski’s type for solving nonlinear equations. J. Appl. Math. 2012, 425867 (2012)

Soleymani, F., Vanani, S.K., Afghani, A.: A general three-step class of optimal iterations for nonlinear equations. Math. Probl. Eng. 2011, 469512 (2011). 10 pp.

Geum, Y.H., Kim, Y.I.: A uniparametric family of three-step eighth-order multipoint iterative methods for simple roots. Appl. Math. Lett. 24, 929–935 (2011)

Geum, Y.H., Kim, Y.I.: A biparametric family of eighth-order methods with their third-step weighting function decomposed into a one-variable linear fraction and a two-variable generic function. Comput. Math. Appl. 61, 708–714 (2011)

Jay, I.O.: A note on Q-order of convergence. BIT Numer. Math. 41, 422–429 (2001)

Chicharro, F., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameters planes of iterative families and methods. Sci. World J. 2013, 780153 (2013). 11 pp.

[-]

recommendations

 

This item appears in the following Collection(s)

Show full item record