Author:
George Santhosh,Argyros Ioannis K
Abstract
The aim of this paper is to extend the radius of convergence and improve the ratio of convergence for a certain class of Euler-Halley type methods with one parameter in a Banach space. These improvements over earlier works are obtained using the same functions as before but more precise information on the location of the iterates. Special cases and examples are also presented in this study.
Publisher
Academia Romana Filiala Cluj
Reference17 articles.
1. Amat, S., Busquier, S., Gutierrez, J.M., Geometric constructions of iterative functions to solve nonlinear equations, J. Comput. Appl. Math., 157 (2003), pp. 197– 205, https://doi.org/10.1016/s0377-0427(03)00420-5
2. Argyros, I.K., On an improved unified convergence analysis for a certain class of Euler-Halley -type methods, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 13, (2006), pp. 207–215.
3. I. K. Argyros D.Chen, Results on the Chebyshev method in Banach spaces, Proyecciones 12, (1993), pp. 119–128, https://doi.org/10.22199/s07160917.1993.0002.00002
4. I. K. Argyros D.Chen, Q. Quian, A convergence analysis for rational methods with a parameter in Banach space, Pure Math. Appl. 5, (1994), pp. 59–73.
5. Argyros, I.K., A.A. Magrenan, Improved local convergence analysis of the Gauss- Newton method under a majorant condition, Computational Optimization and Applications, 60,2(2015), pp. 423–439, https://doi.org/10.1007/s10589-014-9704-6