On the semilocal convergence of Newton–type methods, when the derivative is not continuously invertible
- Ioannis K. Argyros iargyros@cameron.edu
- Saïd Hilout said.hilout@math.univ--poitiers.fr
Downloads
DOI:
https://doi.org/10.4067/S0719-06462011000300001Abstract
We provide a semilocal convergence analysis for Newton–type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Fr´echet– derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton–type methods [1]–[12]. We also provide weaker sufficient convergence conditions, and finer error bound on the distances involved (under the same computational cost) than [1]–[12], in some intersting cases. Numerical examples are also provided in this study.
Keywords
Most read articles by the same author(s)
- Ioannis K. Argyros, Santhosh George, Ball comparison between Jarratt‘s and other fourth order method for solving equations , CUBO, A Mathematical Journal: Vol. 20 No. 3 (2018)
- Ioannis K. Argyros, Saïd Hilout, On the solution of generalized equations and variational inequalities , CUBO, A Mathematical Journal: Vol. 13 No. 1 (2011): CUBO, A Mathematical Journal
- Ioannis K. Argyros, Santhosh George, Extended domain for fifth convergence order schemes , CUBO, A Mathematical Journal: Vol. 23 No. 1 (2021)
- Ioannis K. Argyros, Saïd Hilout, Convergence conditions for the secant method , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal
- Ioannis K. Argyros, An improved convergence and complexity analysis for the interpolatory Newton method , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal