Order of Convergence and Dynamics of Newton–Gauss-Type Methods

On the basis of new iterative technique designed by Zhongli Liu in 2016 with convergence orders three and five, an extension to order six can be found this paper. The study high-convergence-order methods under weak conditions is extreme importance, because higher means that fewer iterations are carried out achieve a predetermined error tolerance. In enhance practicality these Liu, analysis without application Taylor expansion requires operator only two times differentiable, unlike earlier studies. A semilocal provided. Furthermore, numerical experiments verifying criteria, comparative studies dynamics discussed for better interpretation.