On a two-point Newton-like method of convergent order two

Abstract

We introduce a two-point Newton-like iteration with a geometrical interpretation similar to the Secant method which is essentially of quadratic order. A local as well as a semilocal convergence analysis is provided for this method on the basis of the majorant principle. The superiority of this method over others using the same type of hypotheses is established. Some numerical examples show how to choose in practice the operators involved. Finally, the monotone convergence of the method is examined on partially ordered topological spaces.

Keywords:

• Banach space
• POTL space
• Majorizing sequence/principle
• Radius of convergence
• Divided differences of order one and two
• Local/semilocal/monotone convergence
• Two-point method