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: 196

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.

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References

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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

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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

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Articles