Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations
Abstract
In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighth
order have been utilized to establish the convergence of a derivative free class of seventh order
iterative algorithms. Moreover, no error distances or results on uniqueness of the solution were
given. In this study, extended ball convergence analysis is derived for this class by imposing
conditions on the first derivative. Additionally, we offer error distances and convergence radius
together with the region of uniqueness for the solution. Therefore, we enlarge the practical
utility of these algorithms. Also, convergence regions of a specific member of this class are displayed
for solving complex polynomial equations. At the end, standard numerical applications
are provided to illustrate the efficacy of our theoretical findings.
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