Ball convergence for an Aitken-Newton method

Ioannis K. Argyros; Munish Kansal; Vinay Kanwar

doi:10.33993/jnaat472-1082

Authors

Ioannis K. Argyros Cameron University, USA
Munish Kansal Thapar Institute of Engineering and Technology, India
Vinay Kanwar Panjab University, India

DOI:

https://doi.org/10.33993/jnaat472-1082

Keywords:

Nonlinear equations, Aitken-Newton method, local convergence, eighth order of convergence

Abstract views: 314

Abstract

We present a local convergence analysis of an eighth-order Aitken-Newton method for approximating a locally unique solution of a nonlinear equation. Earlier studies have shown convergence of these methods under hypotheses up to the eighth derivative of the function although only the first derivative appears in the method. In this study, we expand the applicability of these methods using only hypotheses up to the first derivative of the function. This way the applicability of these methods is extended under weaker hypotheses. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.

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