On the semi-local convergence of a sixth order method in Banach space





Nonlinear equations, Fréchet-derivative, Semi-local convergence, Banach spaces
Abstract views: 68


High convergence order methods are important in computational mathematics, since they generate sequences converging to a solution of a non-linear equation. The derivation of the order requires Taylor series expansions and the existence of derivatives not appearing on the method. Therefore, these results cannot assure the convergence of the method in those cases when such high order derivatives do not exist. But, the method may converge.

In this article, a process is introduced by which the semi-local convergence analysis of a sixth order method is obtained using only information from the operators on the method. Numerical examples are included to complement the theory.


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How to Cite

Argyros, I. K., John, J. A., & Jayaraman, J. (2022). On the semi-local convergence of a sixth order method in Banach space. J. Numer. Anal. Approx. Theory, 51(2), 144–154. https://doi.org/10.33993/jnaat512-1284