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.

Keywords

• derivative free iterative algorithm;
• order of convergence;
• banach space;
• ball convergence