Accelerating the convergence of Newton-type iterations

Abstract

In this paper, we present a new accelerating procedure in order to speed up the convergence of Newton-type methods. In particular, we derive iterations with a high and optimal order of convergence. This technique can be applied to any iteration with a low order of convergence. As expected, the convergence of the proposed methods was remarkably fast. The effectiveness of this technique is illustrated by numerical experiments.

Keywords

• Newton-type iterations
• accelerating procedure
• convergence order
• efficiency index