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Ball convergence of a sixth-order Newton-like method based on means under weak conditions
(Journal of Mathematical Chemistry, 2018-08)
We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative ...
A variant of Steffensen-King's type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach
(Applied Mathematics and Computation, 2015-02)
First, it is attempted to derive an optimal derivative-free Steffensen-King's type family without memory for computing a simple zero of a nonlinear function with efficiency index 4(1/3) approximate to 1.587. Next, since ...