SciELO - Scientific Electronic Library Online

vol.20 número3Study of global asymptotic stability in nonlinear neutral dynamic equations on time scalesThe basic ergodic theorems, yet again índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google


Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.20 no.3 Temuco oct. 2018 


Ball comparison between Jarratt’s and other fourth order method for solving equations

Ioannis K. Argyros1 

Santhosh George2 

1Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA.

2National Institute of Technology Karnataka, Department of Mathematical and Computational Sciences, India-575 025.


The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt’s fourth order method and another method of the same convergence order.

Keywords and Phrases: Jarratt method; Banach space; Ball convergence


El orden de convergencia de métodos iterativos es determinado usando derivadas de orden alto y series de Taylor, y sin poder entregar cotas de error calculables, resultados de unicidad de soluciones o información de cómo elegir el punto inicial. Tratamos estos problemas usando hipótesis sólo en la primera derivada. Más aún, para responder todos los anteriores, presentamos una técnica que usa una comparación entre el radio de convergencia del método de cuarto orden de Jarratt y otro método con el mismo orden de convergencia.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


[1] Amat, S., Busquier, S., Plaza, S., On two families of high order Newton type methods, Appl. Math. Comput., 25, (2012), 2209-2217. [ Links ]

Amat, S. , Argyros, I. K., Busquier, S. , Hernandez, M. A., On two high-order families of frozen Newton-type methods, Numer., Lin., Alg. Appl., 25 (2018), 1-13. [ Links ]

[3] Argyros, I. K., Ezquerro, J. A., Gutierrez, J. M., Hernandez, M. A. , Hilout, S., On the semilocal convergence of efficient Chebyshev-Secant-type methods, J. Comput. Appl. Math., 235, (2011), 3195-2206. [ Links ]

[4] Argyros, I. K. , George, S., Thapa, N., Mathematical Modeling For The Solution Of Equations And Systems Of Equations With Applications, Volume-I, Nova Publishes, NY, 2018. [ Links ]

[5] Argyros, I. K. , George, S. , Thapa, N. , Mathematical Modeling For The Solution Of Equations And Systems Of Equations With Applications , Volume-II, Nova Publishes, NY , 2018. [ Links ]

[6] I. K. Argyros and S. Hilout Weaker conditions for the convergence of Newton’s method, J. Complexity, 28, (2012), 364-387. [ Links ]

[7] Argyros, I. K, Magréñan, A. A, A contemporary study of iterative methods, Elsevier (Academic Press), New York, 2018. [ Links ]

[8] Argyros, I. K., Magreñán, A. A., Iterative methods and their dynamics with applications, CRC Press, New York, USA, 2017. [ Links ]

[9] Cordero, A., Hueso, J. L., Martinez, E., Torregrosa, J. R., A modified Newton-Jarratt’s composition, Numer. Algorithms, 55, (2010), 87-99. [ Links ]

[10] Kantorovich, L. V., Akilov, G. P., Functional analysis in normed spaces, Pergamon Press, New York, 1982. [ Links ]

[11] Hernandez, M. A. , Martinez, E. , Tervel, C., Semi-local convergence of a k−step iterative process and its application for solving a special kind of conservative problems, Numer. Algor., 76, (2017), 309-331. [ Links ]

[12] Jarratt, P., Some fourth order multipoint iterative methods for solving equations, Math. Comput., 20, (1966), 434-437. [ Links ]

[13] Petkovic, M. S., Neta, B., Petkovic, L., Džunič, J., Multipoint methods for solving nonlinear equations, Elsevier, 2013. [ Links ]

[14] Rheinboldt, W. C., An adaptive continuation process for solving systems of nonlinear equations, Polish Academy of Science, Banach Ctr. Publ. 3 (1978), no. 1, 129-142. [ Links ]

[15] Sharma, J. R., Guha , R. K., Sharma, R., An efficient fourth order weighted Newton method for systems of nonlinear equations, Numer. Algorithm, 62 (2013), 307-323. [ Links ]

[16] J. F. Traub, Iterative methods for the solution of equations, Prentice- Hall Series in Automatic Computation, Englewood Cliffs, N. J., 1964. [ Links ]

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License