Start iteration for Ezquerro-Hernández method

Authors

  • Cristian Mihai Cira Aurel Vlaicu University of Arad, Romania
  • Octavian Cira Aurel Vlaicu University of Arad, Romania

DOI:

https://doi.org/10.33993/jnaat372-885

Keywords:

Ezquerro-Hernández method, start iteration from sphere of quadruple convergence
Abstract views: 192

Abstract

We present a numerical method for solving nonlinear equation systems, namely Ezquerro-Hern\'{a}ndez method with a rate of convergence equal to 4. The main result of this article is an algorithm that determines a start iteration for the method within its quadruple convergence sphere.

Downloads

Download data is not yet available.

References

Cira O. and Măruşter, Şt., Metode numerice pentru ecuaţii neliniare, Ed. Matrix Rom, Bucureşti, 2008 (in Romanian).

Cira, O., Algorithm for determination of initial iteration of numerical methods for the solution of nonlinear equation, An. Universităţii de Vest din Timişoara, Ser. Şti. Mat. XXVI, 3, pp. 17-23, 1988.

Ezquerro, J. A., A study convergence for a fourth-order two-point iteration in Banach spaces, Kodai Math. J., 22, pp. 373-383, 1999, https://doi.org/10.2996/kmj/1138044091 . DOI: https://doi.org/10.2996/kmj/1138044091

Sburlan, S. F., Gradul topologic. Lecţii asupra ecuaţiilor neliniare, Ed. Academiei Romane, Bucureşti, 1983.

Stenger, F., An algorithm for the topological degree of a mapping in n-spaces, Bull. A.M.S., 81, pp. 179-182, 1975, https://doi.org/10.1090/s0002-9904-1975-13698-6. DOI: https://doi.org/10.1090/S0002-9904-1975-13698-6

Vrahatis, M. N., Solving systems of nonlinear equations using the nonzero value of the topological degree, ACM Trans. Math. Softw., 14, no. 4, pp. 312-329, 1988, https://doi.org/10.1145/50063.214384 . DOI: https://doi.org/10.1145/50063.214384

Downloads

Published

2008-08-01

How to Cite

Cira, C. M., & Cira, O. (2008). Start iteration for Ezquerro-Hernández method. Rev. Anal. Numér. Théor. Approx., 37(2), 133–142. https://doi.org/10.33993/jnaat372-885

Issue

Vol. 37 No. 2 (2008)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.